Call Libraries

library(tidyverse)
library(caret)
library(MASS)
library(car)
library(moments)

Calling the Transformed Datasets

Creating the Models

sat.model.summary <- function (df, field, sat.formula){
Warning messages:
1: In overlay(...) :
  reverting 'unnamed.chunk.label' to 'unnamed-chunk' for duration of render
2: In overlay(...) :
  reverting 'unnamed.chunk.label' to 'unnamed-chunk' for duration of render
    
    #Shapiro-Wilks test to evaluate normality
    print(shapiro.test(df[[field]]))
    
    #Kurtosis evaluation (normal distribution has a value close to 3)
    print('kurtosis')
    print(kurtosis(df[[field]]))
    linear.model.cleaned = lm(sat.formula, data = df)
    print(summary(linear.model.cleaned))
    plot(linear.model.cleaned)
    
    #histograms of response variable to check distribution
    print(df %>% 
      ggplot(aes_string(field)) + 
      geom_histogram() + 
      labs(title = 'Average Credit Amount Distribution') + 
      theme(plot.title = element_text(hjust = 0.5)))
    
    #Checking multicollinearity using VIF measurement
    print(vif(linear.model.cleaned))
    influencePlot(linear.model.cleaned)
    #avPlots(linear.model.cleaned)
}


sat.formula <- Avg ~ .
sat.field <- 'Avg'

sat.model.summary(income_cleaned, sat.field, sat.formula)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.17297, p-value < 2.2e-16

[1] "kurtosis"
[1] 169.7518

Call:
lm(formula = sat.formula, data = df)

Residuals:
      Min        1Q    Median        3Q       Max 
-11338570   -547702     94139    421302  87181761 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                                                   -1.157e+08  5.512e+07  -2.100  0.03590 *  
Year                                                                                           5.721e+04  2.731e+04   2.095  0.03634 *  
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                         -3.287e+05  1.242e+06  -0.265  0.79140    
NameAlternative Minimum Tax Credit                                                             6.538e+05  9.757e+05   0.670  0.50286    
NameBeer Production Credit                                                                     3.316e+05  1.290e+06   0.257  0.79715    
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  1.429e+06  9.960e+05   1.434  0.15162    
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     4.098e+06  1.421e+06   2.883  0.00398 ** 
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.182e+06  9.927e+05   1.191  0.23386    
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                             -7.587e+04  9.920e+05  -0.076  0.93904    
NameClean Heating Fuel Credit                                                                  7.148e+04  1.024e+06   0.070  0.94436    
NameConservation Easement Tax Credit                                                           1.143e+05  1.064e+06   0.107  0.91444    
NameCredit for Employment of Persons with Disabilities                                        -9.343e+05  1.119e+06  -0.835  0.40391    
NameCredit for Purchase of an Automated External Defibrillator                                -1.449e+05  9.695e+05  -0.150  0.88117    
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities      2.316e+05  1.779e+06   0.130  0.89645    
NameEmpire State Apprentice Tax Credit                                                        -7.983e+05  1.524e+06  -0.524  0.60040    
NameEmpire State Commercial Production Credit                                                  2.183e+05  1.291e+06   0.169  0.86576    
NameEmpire State Film Post Production Credit                                                   2.521e+04  1.049e+06   0.024  0.98082    
NameEmpire State Film Production Credit                                                        1.145e+07  9.967e+05  11.485  < 2e-16 ***
NameEmpire State Musical and Theatrical Production Credit                                     -2.342e+05  1.775e+06  -0.132  0.89507    
NameExcelsior Jobs Program Credit                                                              1.035e+05  9.545e+05   0.108  0.91366    
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             2.752e+06  8.862e+05   3.105  0.00193 ** 
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   4.845e+05  9.213e+05   0.526  0.59899    
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.245e+06  9.239e+05   1.348  0.17785    
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners          -1.025e+05  9.549e+05  -0.107  0.91455    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                           -6.145e+04  9.387e+05  -0.065  0.94781    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                     9.119e+04  1.044e+06   0.087  0.93038    
NameFarm Workforce Retention Credit                                                           -7.802e+03  1.285e+06  -0.006  0.99516    
NameFarmers' School Tax Credit                                                                 1.440e+05  1.021e+06   0.141  0.88786    
NameHire a Veteran Credit                                                                     -1.238e+06  1.782e+06  -0.695  0.48721    
NameHistoric Properties Rehabilitation Credit                                                  1.352e+06  1.055e+06   1.282  0.20015    
NameIndustrial or Manufacturing Business Tax Credit                                            4.997e+05  1.074e+06   0.465  0.64173    
NameInvestment Tax Credit                                                                      4.463e+05  8.895e+05   0.502  0.61588    
NameInvestment Tax Credit for the Financial Services Industry                                  3.976e+05  1.008e+06   0.395  0.69325    
NameLife Sciences Research & Development Tax Credit                                           -8.207e+04  2.099e+06  -0.039  0.96882    
NameLong-Term Care Insurance Credit                                                            1.246e+05  9.808e+05   0.127  0.89892    
NameLow-Income Housing Credit                                                                 -2.764e+04  1.113e+06  -0.025  0.98020    
NameMinimum Wage Reimbursement Credit                                                         -2.931e+05  1.006e+06  -0.291  0.77075    
NameMortgage Servicing Tax Credit                                                             -4.540e+05  1.085e+06  -0.418  0.67565    
NameNew York Youth Jobs Program Tax Credit                                                    -2.587e+05  9.381e+05  -0.276  0.78279    
NameQETC Capital Tax Credit                                                                    2.616e+05  1.386e+06   0.189  0.85032    
NameQETC Employment Credit                                                                     1.335e+05  1.026e+06   0.130  0.89641    
NameQETC Facilities, Operations, and Training Credit                                           5.153e+05  1.918e+06   0.269  0.78820    
NameReal Property Tax Relief Credit for Manufacturing                                         -2.635e+05  9.654e+05  -0.273  0.78490    
NameSpecial Additional Mortgage Recording Tax Credit                                           3.678e+04  9.244e+05   0.040  0.96827    
NameSTART-UP NY Tax Elimination Credit                                                         4.061e+03  1.130e+06   0.004  0.99713    
Group1,000,000 - 24,999,999                                                                    2.170e+05  3.501e+05   0.620  0.53548    
Group100,000 - 499,999                                                                         1.352e+05  3.579e+05   0.378  0.70572    
Group100,000,000 - 499,999,999                                                                 9.644e+05  3.937e+05   2.449  0.01441 *  
Group25,000,000 - 49,999,999                                                                   4.519e+05  4.223e+05   1.070  0.28474    
Group50,000,000 - 99,999,999                                                                   4.021e+05  4.235e+05   0.950  0.34247    
Group500,000 - 999,999                                                                         2.195e+05  3.880e+05   0.566  0.57170    
Group500,000,000 - and over                                                                    3.073e+06  3.846e+05   7.991 2.33e-15 ***
GroupZero or Net Loss                                                                          9.536e+05  3.339e+05   2.856  0.00433 ** 
Num                                                                                           -4.520e+02  8.569e+02  -0.527  0.59791    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3868000 on 1867 degrees of freedom
Multiple R-squared:  0.2361,    Adjusted R-squared:  0.2144 
F-statistic: 10.88 on 53 and 1867 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.125869  1        1.458036
Name  3.521453 43        1.014746
Group 1.510763  8        1.026124
Num   1.645484  1        1.282764

income.model <- lm(sat.formula, data = income_cleaned)


sat.model.summary(industry_cleaned, sat.field, sat.formula)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.22287, p-value < 2.2e-16

[1] "kurtosis"
[1] 135.5482

Call:
lm(formula = sat.formula, data = df)

Residuals:
      Min        1Q    Median        3Q       Max 
-11581741   -371031    -23164    154182  28917959 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                                                   -3.926e+07  2.051e+07  -1.914 0.055677 .  
Year                                                                                           1.936e+04  1.016e+04   1.905 0.056959 .  
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                          5.584e+04  5.062e+05   0.110 0.912180    
NameAlternative Minimum Tax Credit                                                             3.523e+05  4.208e+05   0.837 0.402556    
NameBeer Production Credit                                                                     8.799e+04  6.261e+05   0.141 0.888249    
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  1.919e+06  4.473e+05   4.290 1.86e-05 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     4.064e+06  7.278e+05   5.584 2.62e-08 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.054e+06  4.779e+05   2.206 0.027462 *  
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                              1.327e+05  4.760e+05   0.279 0.780429    
NameClean Heating Fuel Credit                                                                  2.785e+05  4.595e+05   0.606 0.544549    
NameConservation Easement Tax Credit                                                           2.743e+04  4.700e+05   0.058 0.953457    
NameCredit for Employment of Persons with Disabilities                                         1.574e+05  5.069e+05   0.311 0.756142    
NameCredit for Purchase of an Automated External Defibrillator                                 1.082e+05  4.465e+05   0.242 0.808639    
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities      2.090e+05  8.286e+05   0.252 0.800866    
NameEmpire State Apprentice Tax Credit                                                        -3.324e+05  1.012e+06  -0.329 0.742537    
NameEmpire State Commercial Production Credit                                                  3.524e+05  6.172e+05   0.571 0.568123    
NameEmpire State Film Post Production Credit                                                   5.332e+05  5.224e+05   1.021 0.307585    
NameEmpire State Film Production Credit                                                        1.170e+07  4.785e+05  24.458  < 2e-16 ***
NameEmpire State Musical and Theatrical Production Credit                                      7.676e+04  9.010e+05   0.085 0.932112    
NameExcelsior Jobs Program Credit                                                              7.086e+05  4.393e+05   1.613 0.106849    
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             1.381e+06  4.318e+05   3.199 0.001399 ** 
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   3.715e+05  4.213e+05   0.882 0.377942    
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.160e+06  4.192e+05   2.767 0.005700 ** 
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners           3.634e+05  4.311e+05   0.843 0.399359    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                            2.567e+05  4.265e+05   0.602 0.547350    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                     7.379e+04  5.041e+05   0.146 0.883634    
NameFarm Workforce Retention Credit                                                            2.727e+04  5.352e+05   0.051 0.959361    
NameFarmers' School Tax Credit                                                                 1.287e+05  5.133e+05   0.251 0.802102    
NameHire a Veteran Credit                                                                      1.459e+05  8.253e+05   0.177 0.859709    
NameHistoric Properties Rehabilitation Credit                                                  1.875e+06  4.841e+05   3.874 0.000110 ***
NameInvestment Tax Credit                                                                      7.182e+05  4.129e+05   1.739 0.082075 .  
NameInvestment Tax Credit for the Financial Services Industry                                  6.339e+05  5.757e+05   1.101 0.270913    
NameLife Sciences Research & Development Tax Credit                                           -2.243e+03  9.007e+05  -0.002 0.998014    
NameLong-Term Care Insurance Credit                                                            1.385e+05  4.200e+05   0.330 0.741537    
NameLow-Income Housing Credit                                                                  1.642e+06  5.494e+05   2.988 0.002833 ** 
NameMinimum Wage Reimbursement Credit                                                          9.624e+04  4.381e+05   0.220 0.826159    
NameMortgage Servicing Tax Credit                                                              2.077e+05  6.462e+05   0.321 0.747934    
NameNew York Youth Jobs Program Tax Credit                                                     1.953e+05  4.273e+05   0.457 0.647604    
NameQETC Capital Tax Credit                                                                    2.986e+05  5.868e+05   0.509 0.610823    
NameQETC Employment Credit                                                                     8.982e+04  4.465e+05   0.201 0.840607    
NameQETC Facilities, Operations, and Training Credit                                           3.477e+05  6.711e+05   0.518 0.604441    
NameReal Property Tax Relief Credit for Manufacturing                                          1.520e+05  4.423e+05   0.344 0.731171    
NameSpecial Additional Mortgage Recording Tax Credit                                           2.609e+05  4.432e+05   0.589 0.556155    
NameSTART-UP NY Tax Elimination Credit                                                         1.703e+04  4.750e+05   0.036 0.971411    
GroupAdministrative and Support and Waste Management and Remediation Services                 -2.280e+03  2.519e+05  -0.009 0.992777    
GroupAdministrative/Support/Waste Management/Remediation Services                             -3.173e+03  2.798e+05  -0.011 0.990952    
GroupAgriculture, Forestry, Fishing and Hunting                                                7.269e+04  2.330e+05   0.312 0.755097    
GroupArts, Entertainment, and Recreation                                                       5.866e+05  2.317e+05   2.532 0.011408 *  
GroupConstruction                                                                             -1.699e+04  2.171e+05  -0.078 0.937621    
GroupEducational Services                                                                      5.569e+04  2.948e+05   0.189 0.850176    
GroupFinance and Insurance                                                                     2.139e+05  2.034e+05   1.051 0.293237    
GroupHealth Care and Social Assistance                                                         1.300e+04  2.290e+05   0.057 0.954731    
GroupInformation                                                                              -2.433e+05  2.178e+05  -1.117 0.263917    
GroupManagement of Companies and Enterprises                                                   3.355e+05  1.949e+05   1.721 0.085332 .  
GroupManufacturing                                                                             6.786e+05  2.028e+05   3.346 0.000831 ***
GroupMining                                                                                   -1.561e+04  3.593e+05  -0.043 0.965352    
GroupMining, Quarrying, and Oil and Gas Extraction                                             1.084e+05  3.011e+05   0.360 0.718901    
GroupOther Services (except Public Administration)                                            -6.462e+04  2.217e+05  -0.291 0.770697    
GroupProfessional, Scientific, and Technical Services                                          3.736e+05  2.085e+05   1.792 0.073214 .  
GroupReal Estate and Rental and Leasing                                                        9.506e+04  2.044e+05   0.465 0.641882    
GroupRetail Trade                                                                              4.746e+04  2.036e+05   0.233 0.815756    
GroupTransportation and Warehousing                                                           -1.866e+04  2.300e+05  -0.081 0.935321    
GroupUtilities                                                                                 5.308e+05  2.633e+05   2.016 0.043917 *  
GroupWholesale Trade                                                                           6.106e+04  2.081e+05   0.293 0.769261    
Num                                                                                           -9.657e+02  4.272e+02  -2.260 0.023889 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1612000 on 2411 degrees of freedom
Multiple R-squared:  0.4674,    Adjusted R-squared:  0.4533 
F-statistic: 33.06 on 64 and 2411 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.190806  1        1.480137
Name  5.185764 42        1.019787
Group 2.724217 20        1.025371
Num   1.370920  1        1.170863

industry.model <- lm(sat.formula, data = industry_cleaned)

Correcting violation of Normality in previous model with BoxCox transform

bc_func <- function (lm.cleaned, lambda.range){
  bc = boxCox(lm.cleaned, lambda = lambda.range)
  #Extracting the best lambda value.
  return(bc$x[which(bc$y == max(bc$y))])
}
  
#Income Group Dataset
income.lambda.bc = bc_func(income.model, seq(-0.2, 0.2, 1/10))

income.lambda.bc
[1] -0.01414141
#Industry Group Dataset
industry.lambda.bc = bc_func(industry.model, seq(-0.2, 0.2, 1/10))

industry.lambda.bc
[1] -0.03434343
bc_transform <- function(df, lambda.bc){
  return (df %>% 
            mutate(Avg.bc = (Avg^lambda.bc -1)/lambda.bc) %>% 
            select(-c(Avg, Amount)))
}

#Income Group Dataset
income_cleaned_bc <- bc_transform(income_cleaned, income.lambda.bc)
income.model.bc = lm(Avg.bc ~ ., data = income_cleaned_bc)

#Industry Group Dataset
industry_cleaned_bc <- bc_transform(industry_cleaned, industry.lambda.bc)
industry.model.bc = lm(Avg.bc ~ ., data = industry_cleaned_bc)

Checking linear regression assumptions for the transformed data.

sat.formula.bc <- Avg.bc ~ .
sat.field.bc <- 'Avg.bc'

#Income
sat.model.summary(income_cleaned_bc, sat.field.bc, sat.formula.bc)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.99696, p-value = 0.000782

[1] "kurtosis"
[1] -0.2553313

Call:
lm(formula = sat.formula, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.6597 -0.5738 -0.0113  0.5668  4.4826 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)
(Intercept)                                                                                   -3.634e+01  1.456e+01  -2.496 0.012643
Year                                                                                           2.288e-02  7.214e-03   3.171 0.001543
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                         -8.643e-01  3.281e-01  -2.634 0.008510
NameAlternative Minimum Tax Credit                                                            -2.052e+00  2.577e-01  -7.962 2.91e-15
NameBeer Production Credit                                                                     5.687e-01  3.407e-01   1.669 0.095234
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  1.715e+00  2.630e-01   6.521 8.99e-11
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     2.676e+00  3.754e-01   7.130 1.43e-12
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.331e+00  2.622e-01   5.076 4.24e-07
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                              5.458e-02  2.620e-01   0.208 0.834991
NameClean Heating Fuel Credit                                                                 -3.086e+00  2.705e-01 -11.409  < 2e-16
NameConservation Easement Tax Credit                                                          -2.137e+00  2.810e-01  -7.606 4.45e-14
NameCredit for Employment of Persons with Disabilities                                        -3.118e+00  2.956e-01 -10.547  < 2e-16
NameCredit for Purchase of an Automated External Defibrillator                                -2.938e+00  2.560e-01 -11.473  < 2e-16
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities     -5.673e-01  4.698e-01  -1.207 0.227430
NameEmpire State Apprentice Tax Credit                                                        -2.207e+00  4.024e-01  -5.485 4.71e-08
NameEmpire State Commercial Production Credit                                                  6.075e-02  3.410e-01   0.178 0.858634
NameEmpire State Film Post Production Credit                                                   1.101e+00  2.769e-01   3.977 7.25e-05
NameEmpire State Film Production Credit                                                        2.853e+00  2.632e-01  10.838  < 2e-16
NameEmpire State Musical and Theatrical Production Credit                                      2.508e-01  4.688e-01   0.535 0.592803
NameExcelsior Jobs Program Credit                                                              4.651e-01  2.521e-01   1.845 0.065178
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             8.876e-01  2.341e-01   3.792 0.000154
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   1.775e-01  2.433e-01   0.730 0.465701
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.220e+00  2.440e-01   5.000 6.26e-07
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners           1.182e-01  2.522e-01   0.469 0.639260
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                           -8.497e-01  2.479e-01  -3.427 0.000623
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                    -1.358e+00  2.756e-01  -4.928 9.02e-07
NameFarm Workforce Retention Credit                                                           -1.612e+00  3.394e-01  -4.749 2.20e-06
NameFarmers' School Tax Credit                                                                -1.311e+00  2.696e-01  -4.863 1.26e-06
NameHire a Veteran Credit                                                                     -2.915e+00  4.706e-01  -6.195 7.15e-10
NameHistoric Properties Rehabilitation Credit                                                  1.918e+00  2.786e-01   6.886 7.81e-12
NameIndustrial or Manufacturing Business Tax Credit                                           -1.718e+00  2.836e-01  -6.059 1.66e-09
NameInvestment Tax Credit                                                                      7.147e-02  2.349e-01   0.304 0.760985
NameInvestment Tax Credit for the Financial Services Industry                                  3.176e-01  2.662e-01   1.193 0.232870
NameLife Sciences Research & Development Tax Credit                                            7.033e-01  5.543e-01   1.269 0.204728
NameLong-Term Care Insurance Credit                                                           -2.863e+00  2.590e-01 -11.051  < 2e-16
NameLow-Income Housing Credit                                                                 -9.063e-01  2.940e-01  -3.083 0.002080
NameMinimum Wage Reimbursement Credit                                                         -1.241e+00  2.656e-01  -4.674 3.17e-06
NameMortgage Servicing Tax Credit                                                             -9.378e-01  2.865e-01  -3.273 0.001084
NameNew York Youth Jobs Program Tax Credit                                                    -1.330e+00  2.478e-01  -5.367 9.01e-08
NameQETC Capital Tax Credit                                                                    4.561e-01  3.661e-01   1.246 0.212956
NameQETC Employment Credit                                                                    -5.888e-01  2.709e-01  -2.174 0.029855
NameQETC Facilities, Operations, and Training Credit                                           5.799e-01  5.065e-01   1.145 0.252462
NameReal Property Tax Relief Credit for Manufacturing                                         -1.518e+00  2.550e-01  -5.956 3.09e-09
NameSpecial Additional Mortgage Recording Tax Credit                                          -2.309e-01  2.441e-01  -0.946 0.344374
NameSTART-UP NY Tax Elimination Credit                                                        -2.193e+00  2.985e-01  -7.345 3.05e-13
Group1,000,000 - 24,999,999                                                                    1.090e+00  9.246e-02  11.785  < 2e-16
Group100,000 - 499,999                                                                         3.590e-01  9.451e-02   3.798 0.000150
Group100,000,000 - 499,999,999                                                                 1.685e+00  1.040e-01  16.202  < 2e-16
Group25,000,000 - 49,999,999                                                                   1.325e+00  1.115e-01  11.883  < 2e-16
Group50,000,000 - 99,999,999                                                                   1.473e+00  1.118e-01  13.172  < 2e-16
Group500,000 - 999,999                                                                         6.032e-01  1.025e-01   5.886 4.67e-09
Group500,000,000 - and over                                                                    2.332e+00  1.016e-01  22.953  < 2e-16
GroupZero or Net Loss                                                                          9.934e-01  8.817e-02  11.267  < 2e-16
Num                                                                                           -1.533e-03  2.263e-04  -6.775 1.66e-11
                                                                                                 
(Intercept)                                                                                   *  
Year                                                                                          ** 
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                         ** 
NameAlternative Minimum Tax Credit                                                            ***
NameBeer Production Credit                                                                    .  
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                    ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                      ***
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                                
NameClean Heating Fuel Credit                                                                 ***
NameConservation Easement Tax Credit                                                          ***
NameCredit for Employment of Persons with Disabilities                                        ***
NameCredit for Purchase of an Automated External Defibrillator                                ***
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities        
NameEmpire State Apprentice Tax Credit                                                        ***
NameEmpire State Commercial Production Credit                                                    
NameEmpire State Film Post Production Credit                                                  ***
NameEmpire State Film Production Credit                                                       ***
NameEmpire State Musical and Theatrical Production Credit                                        
NameExcelsior Jobs Program Credit                                                             .  
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                            ***
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                     
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                 ***
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners             
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                           ***
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                    ***
NameFarm Workforce Retention Credit                                                           ***
NameFarmers' School Tax Credit                                                                ***
NameHire a Veteran Credit                                                                     ***
NameHistoric Properties Rehabilitation Credit                                                 ***
NameIndustrial or Manufacturing Business Tax Credit                                           ***
NameInvestment Tax Credit                                                                        
NameInvestment Tax Credit for the Financial Services Industry                                    
NameLife Sciences Research & Development Tax Credit                                              
NameLong-Term Care Insurance Credit                                                           ***
NameLow-Income Housing Credit                                                                 ** 
NameMinimum Wage Reimbursement Credit                                                         ***
NameMortgage Servicing Tax Credit                                                             ** 
NameNew York Youth Jobs Program Tax Credit                                                    ***
NameQETC Capital Tax Credit                                                                      
NameQETC Employment Credit                                                                    *  
NameQETC Facilities, Operations, and Training Credit                                             
NameReal Property Tax Relief Credit for Manufacturing                                         ***
NameSpecial Additional Mortgage Recording Tax Credit                                             
NameSTART-UP NY Tax Elimination Credit                                                        ***
Group1,000,000 - 24,999,999                                                                   ***
Group100,000 - 499,999                                                                        ***
Group100,000,000 - 499,999,999                                                                ***
Group25,000,000 - 49,999,999                                                                  ***
Group50,000,000 - 99,999,999                                                                  ***
Group500,000 - 999,999                                                                        ***
Group500,000,000 - and over                                                                   ***
GroupZero or Net Loss                                                                         ***
Num                                                                                           ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.022 on 1867 degrees of freedom
Multiple R-squared:  0.7368,    Adjusted R-squared:  0.7293 
F-statistic: 98.61 on 53 and 1867 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.125869  1        1.458036
Name  3.521453 43        1.014746
Group 1.510763  8        1.026124
Num   1.645484  1        1.282764

#Industry
sat.model.summary(industry_cleaned_bc, sat.field.bc, sat.formula.bc)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.9902, p-value = 5.826e-12

[1] "kurtosis"
[1] -0.4869026

Call:
lm(formula = sat.formula, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.2888 -0.4697  0.0183  0.4928  3.9068 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)
(Intercept)                                                                                   -6.095e+01  1.107e+01  -5.505 4.09e-08
Year                                                                                           3.440e-02  5.488e-03   6.269 4.30e-10
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                          2.665e-01  2.733e-01   0.975 0.329737
NameAlternative Minimum Tax Credit                                                            -2.463e+00  2.272e-01 -10.839  < 2e-16
NameBeer Production Credit                                                                     6.334e-01  3.381e-01   1.873 0.061126
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  2.198e+00  2.415e-01   9.100  < 2e-16
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     2.727e+00  3.930e-01   6.939 5.06e-12
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.586e+00  2.581e-01   6.148 9.17e-10
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                              9.695e-01  2.570e-01   3.772 0.000166
NameClean Heating Fuel Credit                                                                 -2.544e+00  2.481e-01 -10.252  < 2e-16
NameConservation Easement Tax Credit                                                          -1.123e+00  2.538e-01  -4.423 1.02e-05
NameCredit for Employment of Persons with Disabilities                                        -1.245e+00  2.737e-01  -4.549 5.67e-06
NameCredit for Purchase of an Automated External Defibrillator                                -1.535e+00  2.411e-01  -6.368 2.29e-10
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities     -8.171e-02  4.474e-01  -0.183 0.855119
NameEmpire State Apprentice Tax Credit                                                        -8.683e-01  5.464e-01  -1.589 0.112125
NameEmpire State Commercial Production Credit                                                  6.235e-01  3.333e-01   1.871 0.061481
NameEmpire State Film Post Production Credit                                                   1.439e+00  2.821e-01   5.100 3.66e-07
NameEmpire State Film Production Credit                                                        3.232e+00  2.584e-01  12.509  < 2e-16
NameEmpire State Musical and Theatrical Production Credit                                      1.012e+00  4.865e-01   2.080 0.037608
NameExcelsior Jobs Program Credit                                                              1.643e+00  2.372e-01   6.929 5.42e-12
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             1.310e+00  2.332e-01   5.617 2.17e-08
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   7.127e-01  2.275e-01   3.133 0.001750
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.707e+00  2.264e-01   7.540 6.61e-14
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners           9.777e-01  2.328e-01   4.200 2.77e-05
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                            1.609e-01  2.303e-01   0.699 0.484921
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                    -5.241e-01  2.722e-01  -1.925 0.054320
NameFarm Workforce Retention Credit                                                           -8.623e-01  2.890e-01  -2.984 0.002876
NameFarmers' School Tax Credit                                                                -1.158e+00  2.771e-01  -4.179 3.03e-05
NameHire a Veteran Credit                                                                     -1.040e+00  4.456e-01  -2.335 0.019638
NameHistoric Properties Rehabilitation Credit                                                  2.397e+00  2.614e-01   9.172  < 2e-16
NameInvestment Tax Credit                                                                      6.981e-01  2.230e-01   3.131 0.001763
NameInvestment Tax Credit for the Financial Services Industry                                  1.560e+00  3.108e-01   5.019 5.59e-07
NameLife Sciences Research & Development Tax Credit                                            9.057e-01  4.864e-01   1.862 0.062697
NameLong-Term Care Insurance Credit                                                           -1.867e+00  2.268e-01  -8.231 3.01e-16
NameLow-Income Housing Credit                                                                  1.331e+00  2.967e-01   4.487 7.57e-06
NameMinimum Wage Reimbursement Credit                                                         -9.161e-01  2.366e-01  -3.872 0.000111
NameMortgage Servicing Tax Credit                                                              8.932e-01  3.489e-01   2.560 0.010534
NameNew York Youth Jobs Program Tax Credit                                                     1.263e-01  2.307e-01   0.548 0.584069
NameQETC Capital Tax Credit                                                                    1.162e+00  3.168e-01   3.667 0.000251
NameQETC Employment Credit                                                                    -3.048e-01  2.411e-01  -1.264 0.206249
NameQETC Facilities, Operations, and Training Credit                                           1.147e+00  3.624e-01   3.165 0.001571
NameReal Property Tax Relief Credit for Manufacturing                                         -6.559e-01  2.388e-01  -2.746 0.006077
NameSpecial Additional Mortgage Recording Tax Credit                                           7.505e-01  2.393e-01   3.136 0.001736
NameSTART-UP NY Tax Elimination Credit                                                        -1.834e+00  2.565e-01  -7.151 1.14e-12
GroupAdministrative and Support and Waste Management and Remediation Services                  2.878e-01  1.360e-01   2.116 0.034417
GroupAdministrative/Support/Waste Management/Remediation Services                              1.675e-01  1.511e-01   1.109 0.267612
GroupAgriculture, Forestry, Fishing and Hunting                                               -1.132e-01  1.258e-01  -0.899 0.368486
GroupArts, Entertainment, and Recreation                                                       5.595e-01  1.251e-01   4.473 8.09e-06
GroupConstruction                                                                             -4.299e-02  1.172e-01  -0.367 0.713860
GroupEducational Services                                                                      2.253e-01  1.592e-01   1.415 0.157160
GroupFinance and Insurance                                                                     5.350e-01  1.099e-01   4.870 1.19e-06
GroupHealth Care and Social Assistance                                                        -6.777e-02  1.237e-01  -0.548 0.583720
GroupInformation                                                                               7.098e-01  1.176e-01   6.037 1.81e-09
GroupManagement of Companies and Enterprises                                                   6.672e-01  1.052e-01   6.340 2.73e-10
GroupManufacturing                                                                             4.608e-01  1.095e-01   4.208 2.67e-05
GroupMining                                                                                    2.515e-01  1.940e-01   1.296 0.194977
GroupMining, Quarrying, and Oil and Gas Extraction                                             3.869e-01  1.626e-01   2.379 0.017421
GroupOther Services (except Public Administration)                                            -1.550e-01  1.197e-01  -1.295 0.195482
GroupProfessional, Scientific, and Technical Services                                          4.875e-01  1.126e-01   4.331 1.55e-05
GroupReal Estate and Rental and Leasing                                                        1.461e-01  1.104e-01   1.324 0.185596
GroupRetail Trade                                                                              3.754e-01  1.100e-01   3.414 0.000650
GroupTransportation and Warehousing                                                            2.125e-01  1.242e-01   1.711 0.087179
GroupUtilities                                                                                 6.972e-01  1.422e-01   4.904 1.00e-06
GroupWholesale Trade                                                                           4.367e-01  1.124e-01   3.886 0.000105
Num                                                                                            4.542e-04  2.307e-04   1.969 0.049082
                                                                                                 
(Intercept)                                                                                   ***
Year                                                                                          ***
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                            
NameAlternative Minimum Tax Credit                                                            ***
NameBeer Production Credit                                                                    .  
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                    ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                      ***
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                             ***
NameClean Heating Fuel Credit                                                                 ***
NameConservation Easement Tax Credit                                                          ***
NameCredit for Employment of Persons with Disabilities                                        ***
NameCredit for Purchase of an Automated External Defibrillator                                ***
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities        
NameEmpire State Apprentice Tax Credit                                                           
NameEmpire State Commercial Production Credit                                                 .  
NameEmpire State Film Post Production Credit                                                  ***
NameEmpire State Film Production Credit                                                       ***
NameEmpire State Musical and Theatrical Production Credit                                     *  
NameExcelsior Jobs Program Credit                                                             ***
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                            ***
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                  ** 
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                 ***
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners          ***
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                              
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                    .  
NameFarm Workforce Retention Credit                                                           ** 
NameFarmers' School Tax Credit                                                                ***
NameHire a Veteran Credit                                                                     *  
NameHistoric Properties Rehabilitation Credit                                                 ***
NameInvestment Tax Credit                                                                     ** 
NameInvestment Tax Credit for the Financial Services Industry                                 ***
NameLife Sciences Research & Development Tax Credit                                           .  
NameLong-Term Care Insurance Credit                                                           ***
NameLow-Income Housing Credit                                                                 ***
NameMinimum Wage Reimbursement Credit                                                         ***
NameMortgage Servicing Tax Credit                                                             *  
NameNew York Youth Jobs Program Tax Credit                                                       
NameQETC Capital Tax Credit                                                                   ***
NameQETC Employment Credit                                                                       
NameQETC Facilities, Operations, and Training Credit                                          ** 
NameReal Property Tax Relief Credit for Manufacturing                                         ** 
NameSpecial Additional Mortgage Recording Tax Credit                                          ** 
NameSTART-UP NY Tax Elimination Credit                                                        ***
GroupAdministrative and Support and Waste Management and Remediation Services                 *  
GroupAdministrative/Support/Waste Management/Remediation Services                                
GroupAgriculture, Forestry, Fishing and Hunting                                                  
GroupArts, Entertainment, and Recreation                                                      ***
GroupConstruction                                                                                
GroupEducational Services                                                                        
GroupFinance and Insurance                                                                    ***
GroupHealth Care and Social Assistance                                                           
GroupInformation                                                                              ***
GroupManagement of Companies and Enterprises                                                  ***
GroupManufacturing                                                                            ***
GroupMining                                                                                      
GroupMining, Quarrying, and Oil and Gas Extraction                                            *  
GroupOther Services (except Public Administration)                                               
GroupProfessional, Scientific, and Technical Services                                         ***
GroupReal Estate and Rental and Leasing                                                          
GroupRetail Trade                                                                             ***
GroupTransportation and Warehousing                                                           .  
GroupUtilities                                                                                ***
GroupWholesale Trade                                                                          ***
Num                                                                                           *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.8703 on 2411 degrees of freedom
Multiple R-squared:  0.7631,    Adjusted R-squared:  0.7569 
F-statistic: 121.4 on 64 and 2411 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.190806  1        1.480137
Name  5.185764 42        1.019787
Group 2.724217 20        1.025371
Num   1.370920  1        1.170863

BIC comparison before and after BoxCox transform

BIC(income.model.bc, income.model)
BIC(industry.model.bc, industry.model)

Stepwise Regression on Income_cat_bc (boxcox transformed dataset)

#creating dummy variable columns for stepwise
dummy_func <- function (df){
  x = model.matrix(Avg.bc ~., df)[, -1]
  dummy_bc = as.data.frame(x) %>% mutate(Avg.bc = df$Avg.bc)
  #colnames(dummy_bc) <- str_replace_all(colnames(dummy_bc), "-|'|/| |,|�|&" , '_')
  colnames(dummy_bc) <- str_replace_all(colnames(dummy_bc), "[-'/ ,�&()`]" , '_')
  return(dummy_bc)
}

Cleaning column names further so stepwise regression doesn’t present any errors

#Income Group Dataset
income.dummy.bc <- dummy_func(income_cleaned_bc)
#colnames(income.dummy.bc)[37] <- 'NameManufactureru0092s_Real_Property_Tax_Credit'
colnames(income.dummy.bc)
 [1] "Year"                                                                                         
 [2] "NameAlternative_Fuels_and_Electric_Vehicle_Recharging_Property_Credit"                        
 [3] "NameAlternative_Minimum_Tax_Credit"                                                           
 [4] "NameBeer_Production_Credit"                                                                   
 [5] "NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_6_23_08_but_before_7_1_15"
 [6] "NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_7_1_15"                   
 [7] "NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___Prior_to_6_23_08"                     
 [8] "NameBrownfield_Tax_Credits___Remediation_Real_Property_Tax_Credit"                            
 [9] "NameClean_Heating_Fuel_Credit"                                                                
[10] "NameConservation_Easement_Tax_Credit"                                                         
[11] "NameCredit_for_Employment_of_Persons_with_Disabilities"                                       
[12] "NameCredit_for_Purchase_of_an_Automated_External_Defibrillator"                               
[13] "NameCredit_for_Taxicabs___Livery_Service_Vehicles_Accessible_to_Persons_with_Disabilities"    
[14] "NameEmpire_State_Apprentice_Tax_Credit"                                                       
[15] "NameEmpire_State_Commercial_Production_Credit"                                                
[16] "NameEmpire_State_Film_Post_Production_Credit"                                                 
[17] "NameEmpire_State_Film_Production_Credit"                                                      
[18] "NameEmpire_State_Musical_and_Theatrical_Production_Credit"                                    
[19] "NameExcelsior_Jobs_Program_Credit"                                                            
[20] "NameEZ_QEZE_Tax_Credits___EZ_Investment_Tax_Credit"                                           
[21] "NameEZ_QEZE_Tax_Credits___EZ_Wage_Tax_Credit"                                                 
[22] "NameEZ_QEZE_Tax_Credits___QEZE_Credit_for_Real_Property_Taxes"                                
[23] "NameEZ_QEZE_Tax_Credits___QEZE_Credit_for_Real_Property_Taxes_For_Corporate_Partners"         
[24] "NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit"                                          
[25] "NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit_For_Corporate_Partners"                   
[26] "NameFarm_Workforce_Retention_Credit"                                                          
[27] "NameFarmers__School_Tax_Credit"                                                               
[28] "NameHire_a_Veteran_Credit"                                                                    
[29] "NameHistoric_Properties_Rehabilitation_Credit"                                                
[30] "NameIndustrial_or_Manufacturing_Business_Tax_Credit"                                          
[31] "NameInvestment_Tax_Credit"                                                                    
[32] "NameInvestment_Tax_Credit_for_the_Financial_Services_Industry"                                
[33] "NameLife_Sciences_Research___Development_Tax_Credit"                                          
[34] "NameLong_Term_Care_Insurance_Credit"                                                          
[35] "NameLow_Income_Housing_Credit"                                                                
[36] "NameMinimum_Wage_Reimbursement_Credit"                                                        
[37] "NameMortgage_Servicing_Tax_Credit"                                                            
[38] "NameNew_York_Youth_Jobs_Program_Tax_Credit"                                                   
[39] "NameQETC_Capital_Tax_Credit"                                                                  
[40] "NameQETC_Employment_Credit"                                                                   
[41] "NameQETC_Facilities__Operations__and_Training_Credit"                                         
[42] "NameReal_Property_Tax_Relief_Credit_for_Manufacturing"                                        
[43] "NameSpecial_Additional_Mortgage_Recording_Tax_Credit"                                         
[44] "NameSTART_UP_NY_Tax_Elimination_Credit"                                                       
[45] "Group1_000_000___24_999_999"                                                                  
[46] "Group100_000___499_999"                                                                       
[47] "Group100_000_000___499_999_999"                                                               
[48] "Group25_000_000___49_999_999"                                                                 
[49] "Group50_000_000___99_999_999"                                                                 
[50] "Group500_000___999_999"                                                                       
[51] "Group500_000_000___and_over"                                                                  
[52] "GroupZero_or_Net_Loss"                                                                        
[53] "Num"                                                                                          
[54] "Avg.bc"                                                                                       
#Industry Group Dataset
industry.dummy.bc <- dummy_func(industry_cleaned_bc)
#colnames(industry.dummy.bc)[35] <- 'NameManufactureru0092s_Real_Property_Tax_Credit'
colnames(industry.dummy.bc)
 [1] "Year"                                                                                         
 [2] "NameAlternative_Fuels_and_Electric_Vehicle_Recharging_Property_Credit"                        
 [3] "NameAlternative_Minimum_Tax_Credit"                                                           
 [4] "NameBeer_Production_Credit"                                                                   
 [5] "NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_6_23_08_but_before_7_1_15"
 [6] "NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_7_1_15"                   
 [7] "NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___Prior_to_6_23_08"                     
 [8] "NameBrownfield_Tax_Credits___Remediation_Real_Property_Tax_Credit"                            
 [9] "NameClean_Heating_Fuel_Credit"                                                                
[10] "NameConservation_Easement_Tax_Credit"                                                         
[11] "NameCredit_for_Employment_of_Persons_with_Disabilities"                                       
[12] "NameCredit_for_Purchase_of_an_Automated_External_Defibrillator"                               
[13] "NameCredit_for_Taxicabs___Livery_Service_Vehicles_Accessible_to_Persons_with_Disabilities"    
[14] "NameEmpire_State_Apprentice_Tax_Credit"                                                       
[15] "NameEmpire_State_Commercial_Production_Credit"                                                
[16] "NameEmpire_State_Film_Post_Production_Credit"                                                 
[17] "NameEmpire_State_Film_Production_Credit"                                                      
[18] "NameEmpire_State_Musical_and_Theatrical_Production_Credit"                                    
[19] "NameExcelsior_Jobs_Program_Credit"                                                            
[20] "NameEZ_QEZE_Tax_Credits___EZ_Investment_Tax_Credit"                                           
[21] "NameEZ_QEZE_Tax_Credits___EZ_Wage_Tax_Credit"                                                 
[22] "NameEZ_QEZE_Tax_Credits___QEZE_Credit_for_Real_Property_Taxes"                                
[23] "NameEZ_QEZE_Tax_Credits___QEZE_Credit_for_Real_Property_Taxes_For_Corporate_Partners"         
[24] "NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit"                                          
[25] "NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit_For_Corporate_Partners"                   
[26] "NameFarm_Workforce_Retention_Credit"                                                          
[27] "NameFarmers__School_Tax_Credit"                                                               
[28] "NameHire_a_Veteran_Credit"                                                                    
[29] "NameHistoric_Properties_Rehabilitation_Credit"                                                
[30] "NameInvestment_Tax_Credit"                                                                    
[31] "NameInvestment_Tax_Credit_for_the_Financial_Services_Industry"                                
[32] "NameLife_Sciences_Research___Development_Tax_Credit"                                          
[33] "NameLong_Term_Care_Insurance_Credit"                                                          
[34] "NameLow_Income_Housing_Credit"                                                                
[35] "NameMinimum_Wage_Reimbursement_Credit"                                                        
[36] "NameMortgage_Servicing_Tax_Credit"                                                            
[37] "NameNew_York_Youth_Jobs_Program_Tax_Credit"                                                   
[38] "NameQETC_Capital_Tax_Credit"                                                                  
[39] "NameQETC_Employment_Credit"                                                                   
[40] "NameQETC_Facilities__Operations__and_Training_Credit"                                         
[41] "NameReal_Property_Tax_Relief_Credit_for_Manufacturing"                                        
[42] "NameSpecial_Additional_Mortgage_Recording_Tax_Credit"                                         
[43] "NameSTART_UP_NY_Tax_Elimination_Credit"                                                       
[44] "GroupAdministrative_and_Support_and_Waste_Management_and_Remediation_Services"                
[45] "GroupAdministrative_Support_Waste_Management_Remediation_Services"                            
[46] "GroupAgriculture__Forestry__Fishing_and_Hunting"                                              
[47] "GroupArts__Entertainment__and_Recreation"                                                     
[48] "GroupConstruction"                                                                            
[49] "GroupEducational_Services"                                                                    
[50] "GroupFinance_and_Insurance"                                                                   
[51] "GroupHealth_Care_and_Social_Assistance"                                                       
[52] "GroupInformation"                                                                             
[53] "GroupManagement_of_Companies_and_Enterprises"                                                 
[54] "GroupManufacturing"                                                                           
[55] "GroupMining"                                                                                  
[56] "GroupMining__Quarrying__and_Oil_and_Gas_Extraction"                                           
[57] "GroupOther_Services__except_Public_Administration_"                                           
[58] "GroupProfessional__Scientific__and_Technical_Services"                                        
[59] "GroupReal_Estate_and_Rental_and_Leasing"                                                      
[60] "GroupRetail_Trade"                                                                            
[61] "GroupTransportation_and_Warehousing"                                                          
[62] "GroupUtilities"                                                                               
[63] "GroupWholesale_Trade"                                                                         
[64] "Num"                                                                                          
[65] "Avg.bc"                                                                                       

Stepwise regression using BIC as the criteria (k = log(n)).

#Creating Stepwise Models
bcs = list(income = income.dummy.bc, industry = industry.dummy.bc)
model.fulls = list(income = lm(Avg.bc ~ ., data = income.dummy.bc), industry = lm(Avg.bc ~ ., data = industry.dummy.bc)) #All variables
model.emptys = list(income = lm(Avg.bc ~ 1, data = income.dummy.bc), industry = lm(Avg.bc ~ 1, data = industry.dummy.bc)) #intercept only
k = c('income', 'industry')
forwardBIC = list(income = NULL, industry = NULL)
backwardBIC = list(income = NULL, industry = NULL)

for (i in k){
  bc = bcs[[i]]
  scope = list(lower = formula(model.emptys[[i]]), upper = formula(model.fulls[[i]]))
  n_obs = bc %>% count() %>% dplyr::first()
  forwardBIC[[i]] = step(model.emptys[[i]], scope, direction = "forward", k = log(n_obs))
  backwardBIC[[i]] = step(model.fulls[[i]], scope, direction = "backward", k = log(n_obs))
}

Selecting Best Formula per Dataset from Stepwise Regressions

bic_func <- function (BIC.model){
  print('Adjusted R Squared:')
  print(summary(BIC.model)$adj.r.squared)
  print('Number of Coefficients:')
  print(dim(summary(BIC.model)$coefficient)[1])
  print('VIF Check: ')
  print(max(vif(BIC.model)))
  print("*************************")
}

bic_func(forwardBIC[['income']])
[1] "Adjusted R Squared:"
[1] 0.7287541
[1] "Number of Coefficients:"
[1] 41
[1] "VIF Check: "
[1] 1.867767
[1] "*************************"
bic_func(backwardBIC[['income']])
[1] "Adjusted R Squared:"
[1] 0.7287541
[1] "Number of Coefficients:"
[1] 41
[1] "VIF Check: "
[1] 1.867767
[1] "*************************"
bic_func(forwardBIC[['industry']]) 
[1] "Adjusted R Squared:"
[1] 0.7532731
[1] "Number of Coefficients:"
[1] 42
[1] "VIF Check: "
[1] 1.594046
[1] "*************************"
bic_func(backwardBIC[['industry']])
[1] "Adjusted R Squared:"
[1] 0.7527448
[1] "Number of Coefficients:"
[1] 43
[1] "VIF Check: "
[1] 2.244589
[1] "*************************"
#Manual reduction of variables using VIF and then checked versus saturated model with Anova. This was not used because the saturated model contained multicollinearity issues as indicated by a high VIF score on some coefficients. And the anova test suggested that the coefficients removed in the reduced model were informative in our model, so we couldn't use it either. Thus Stepwise reduction is the preferred method for best model fit.

# VIF.variables <- as.data.frame(vif(model.fulls[['industry']])) %>% 
#   select(VIF = `vif(model.fulls[["industry"]])`) %>% 
#   filter(VIF > 5) %>% rownames()
# 
# industry.dummy.bc.VIF <- industry.dummy.bc %>% select(-all_of(VIF.variables))
# industry.model.VIF <- lm(Avg.bc ~ ., data = industry.dummy.bc.VIF)
# summary(industry.model.VIF)
# anova(industry.model.VIF, model.fulls[['industry']])

Best Model Selection from Stepwise

#The Best Models selected for both income and industry were forwardBIC.

#Income Group Dataset
income.best.formula <- forwardBIC[['income']]$call[[2]]
income.best.formula

#Industry Group Dataset
industry.best.formula <- forwardBIC[['industry']]$call[[2]]
industry.best.formula

Splitting data up into test data and training data (test data is for year 2019, training is the rest)

test_train_split <- function(dummy_bc, best.formula) {
  # data.test <- dummy_bc %>% filter(Year == 2019)
  # data.train <- dummy_bc %>% filter(Year != 2019)
  X <- model.matrix(best.formula, data = dummy_bc)[,-1]
  y <- as.matrix(dummy_bc %>% select(all.vars(best.formula)[1]))
  
  set.seed(0)
  train.i = sample(1:nrow(dummy_bc), 0.8*nrow(dummy_bc), replace = F)
  
  #train
  X.train <- X[train.i,]
  y.train <- y[train.i,]
  
  #test
  X.test <- X[-train.i,]
  y.test <- y[-train.i,]
  
  data.train <- as.data.frame(cbind(y.train, X.train))
  data.test <- as.data.frame(cbind(y.test, X.test))
  colnames(data.train)[1] = all.vars(best.formula)[1]
  colnames(data.test)[1] = all.vars(best.formula)[1]
  
  return (list('X.train' = X.train, 'y.train' = y.train, 'X.test' = X.test, 'y.test' = y.test, 'data.train' = data.train, 'data.test' = data.test))
}
test_train_split(income_cleaned, sat.formula)
$X.train
     Year NameAlternative Fuels and Electric Vehicle Recharging Property Credit NameAlternative Minimum Tax Credit NameBeer Production Credit
1422 2011                                                                     0                                  0                          0
1017 2014                                                                     0                                  0                          0
1860 2002                                                                     0                                  0                          0
679  2016                                                                     0                                  0                          0
129  2019                                                                     0                                  0                          0
930  2015                                                                     0                                  0                          0
1533 2011                                                                     0                                  0                          0
471  2017                                                                     0                                  0                          0
299  2018                                                                     0                                  0                          0
270  2018                                                                     0                                  0                          0
1211 2013                                                                     0                                  0                          0
1331 2012                                                                     0                                  0                          0
597  2016                                                                     0                                  0                          0
1301 2012                                                                     0                                  0                          0
1898 2001                                                                     0                                  0                          0
1518 2011                                                                     0                                  0                          0
330  2018                                                                     0                                  0                          0
1799 2003                                                                     0                                  1                          0
     NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15
1422                                                                                             0
1017                                                                                             0
1860                                                                                             0
679                                                                                              0
129                                                                                              0
930                                                                                              0
1533                                                                                             0
471                                                                                              0
299                                                                                              0
270                                                                                              0
1211                                                                                             0
1331                                                                                             0
597                                                                                              0
1301                                                                                             0
1898                                                                                             0
1518                                                                                             0
330                                                                                              0
1799                                                                                             0
     NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15 NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08
1422                                                                          0                                                                        0
1017                                                                          0                                                                        0
1860                                                                          0                                                                        0
679                                                                           0                                                                        0
129                                                                           0                                                                        0
930                                                                           0                                                                        0
1533                                                                          0                                                                        0
471                                                                           0                                                                        0
299                                                                           0                                                                        0
270                                                                           0                                                                        0
1211                                                                          0                                                                        0
1331                                                                          0                                                                        0
597                                                                           0                                                                        0
1301                                                                          0                                                                        0
1898                                                                          0                                                                        0
1518                                                                          0                                                                        0
330                                                                           0                                                                        0
1799                                                                          0                                                                        0
     NameBrownfield Tax Credits - Remediation Real Property Tax Credit NameClean Heating Fuel Credit NameConservation Easement Tax Credit
1422                                                                 1                             0                                    0
1017                                                                 0                             0                                    0
1860                                                                 0                             0                                    0
679                                                                  0                             0                                    0
129                                                                  0                             0                                    0
930                                                                  0                             0                                    0
1533                                                                 0                             0                                    0
471                                                                  0                             0                                    0
299                                                                  0                             0                                    0
270                                                                  0                             0                                    0
1211                                                                 0                             0                                    0
1331                                                                 0                             0                                    0
597                                                                  0                             0                                    0
1301                                                                 0                             0                                    0
1898                                                                 0                             0                                    0
1518                                                                 0                             0                                    0
330                                                                  0                             0                                    0
1799                                                                 0                             0                                    0
     NameCredit for Employment of Persons with Disabilities NameCredit for Purchase of an Automated External Defibrillator
1422                                                      0                                                              0
1017                                                      0                                                              0
1860                                                      0                                                              0
679                                                       0                                                              0
129                                                       0                                                              0
930                                                       0                                                              0
1533                                                      0                                                              0
471                                                       0                                                              0
299                                                       0                                                              0
270                                                       0                                                              0
1211                                                      0                                                              0
1331                                                      0                                                              0
597                                                       0                                                              0
1301                                                      0                                                              0
1898                                                      0                                                              0
1518                                                      0                                                              0
330                                                       0                                                              0
1799                                                      0                                                              0
     NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities NameEmpire State Apprentice Tax Credit
1422                                                                                         0                                      0
1017                                                                                         0                                      0
1860                                                                                         0                                      0
679                                                                                          0                                      0
129                                                                                          0                                      0
930                                                                                          0                                      0
1533                                                                                         0                                      0
471                                                                                          0                                      0
299                                                                                          0                                      0
270                                                                                          0                                      0
1211                                                                                         0                                      0
1331                                                                                         0                                      0
597                                                                                          0                                      0
1301                                                                                         0                                      0
1898                                                                                         0                                      0
1518                                                                                         0                                      0
330                                                                                          0                                      0
1799                                                                                         0                                      0
     NameEmpire State Commercial Production Credit NameEmpire State Film Post Production Credit NameEmpire State Film Production Credit
1422                                             0                                            0                                       0
1017                                             0                                            0                                       0
1860                                             0                                            0                                       0
679                                              0                                            0                                       0
129                                              0                                            0                                       0
930                                              0                                            0                                       0
1533                                             0                                            0                                       0
471                                              0                                            0                                       0
299                                              0                                            0                                       0
270                                              0                                            0                                       0
1211                                             0                                            0                                       0
1331                                             0                                            0                                       0
597                                              0                                            0                                       1
1301                                             0                                            0                                       1
1898                                             0                                            0                                       0
1518                                             0                                            0                                       0
330                                              0                                            0                                       0
1799                                             0                                            0                                       0
     NameEmpire State Musical and Theatrical Production Credit NameExcelsior Jobs Program Credit NameEZ/QEZE Tax Credits - EZ Investment Tax Credit
1422                                                         0                                 0                                                  0
1017                                                         0                                 0                                                  0
1860                                                         0                                 0                                                  0
679                                                          0                                 0                                                  0
129                                                          0                                 0                                                  0
930                                                          0                                 0                                                  0
1533                                                         0                                 0                                                  0
471                                                          0                                 0                                                  0
299                                                          0                                 0                                                  0
270                                                          0                                 0                                                  0
1211                                                         0                                 0                                                  0
1331                                                         0                                 0                                                  0
597                                                          0                                 0                                                  0
1301                                                         0                                 0                                                  0
1898                                                         0                                 0                                                  0
1518                                                         0                                 0                                                  0
330                                                          0                                 0                                                  0
1799                                                         0                                 0                                                  0
     NameEZ/QEZE Tax Credits - EZ Wage Tax Credit NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes
1422                                            0                                                             0
1017                                            1                                                             0
1860                                            1                                                             0
679                                             0                                                             0
129                                             0                                                             0
930                                             0                                                             0
1533                                            0                                                             0
471                                             0                                                             0
299                                             0                                                             0
270                                             0                                                             0
1211                                            0                                                             0
1331                                            0                                                             1
597                                             0                                                             0
1301                                            0                                                             0
1898                                            1                                                             0
1518                                            0                                                             0
330                                             0                                                             0
1799                                            0                                                             0
     NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit
1422                                                                                    0                                                   0
1017                                                                                    0                                                   0
1860                                                                                    0                                                   0
679                                                                                     0                                                   0
129                                                                                     0                                                   0
930                                                                                     0                                                   0
1533                                                                                    0                                                   0
471                                                                                     0                                                   0
299                                                                                     0                                                   0
270                                                                                     0                                                   0
1211                                                                                    0                                                   0
1331                                                                                    0                                                   0
597                                                                                     0                                                   0
1301                                                                                    0                                                   0
1898                                                                                    0                                                   0
1518                                                                                    0                                                   0
330                                                                                     0                                                   0
1799                                                                                    0                                                   0
     NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners NameFarm Workforce Retention Credit NameFarmers' School Tax Credit
1422                                                                          0                                   0                              0
1017                                                                          0                                   0                              0
1860                                                                          0                                   0                              0
679                                                                           0                                   0                              0
129                                                                           0                                   0                              0
930                                                                           0                                   0                              0
1533                                                                          0                                   0                              0
471                                                                           0                                   0                              0
299                                                                           0                                   0                              0
270                                                                           0                                   0                              1
1211                                                                          1                                   0                              0
1331                                                                          0                                   0                              0
597                                                                           0                                   0                              0
1301                                                                          0                                   0                              0
1898                                                                          0                                   0                              0
1518                                                                          0                                   0                              0
330                                                                           0                                   0                              0
1799                                                                          0                                   0                              0
     NameHire a Veteran Credit NameHistoric Properties Rehabilitation Credit NameIndustrial or Manufacturing Business Tax Credit
1422                         0                                             0                                                   0
1017                         0                                             0                                                   0
1860                         0                                             0                                                   0
679                          0                                             0                                                   0
129                          0                                             0                                                   0
930                          0                                             0                                                   0
1533                         0                                             0                                                   0
471                          0                                             0                                                   0
299                          0                                             0                                                   0
270                          0                                             0                                                   0
1211                         0                                             0                                                   0
1331                         0                                             0                                                   0
597                          0                                             0                                                   0
1301                         0                                             0                                                   0
1898                         0                                             0                                                   0
1518                         0                                             0                                                   0
330                          0                                             0                                                   0
1799                         0                                             0                                                   0
     NameInvestment Tax Credit NameInvestment Tax Credit for the Financial Services Industry NameLife Sciences Research & Development Tax Credit
1422                         0                                                             0                                                   0
1017                         0                                                             0                                                   0
1860                         0                                                             0                                                   0
679                          0                                                             0                                                   0
129                          0                                                             0                                                   0
930                          0                                                             0                                                   0
1533                         0                                                             0                                                   0
471                          1                                                             0                                                   0
299                          0                                                             0                                                   0
270                          0                                                             0                                                   0
1211                         0                                                             0                                                   0
1331                         0                                                             0                                                   0
597                          0                                                             0                                                   0
1301                         0                                                             0                                                   0
1898                         0                                                             0                                                   0
1518                         0                                                             1                                                   0
330                          0                                                             0                                                   0
1799                         0                                                             0                                                   0
     NameLong-Term Care Insurance Credit NameLow-Income Housing Credit NameMinimum Wage Reimbursement Credit NameMortgage Servicing Tax Credit
1422                                   0                             0                                     0                                 0
1017                                   0                             0                                     0                                 0
1860                                   0                             0                                     0                                 0
679                                    1                             0                                     0                                 0
129                                    0                             0                                     0                                 0
930                                    0                             0                                     0                                 0
1533                                   0                             0                                     0                                 0
471                                    0                             0                                     0                                 0
299                                    0                             1                                     0                                 0
270                                    0                             0                                     0                                 0
1211                                   0                             0                                     0                                 0
1331                                   0                             0                                     0                                 0
597                                    0                             0                                     0                                 0
1301                                   0                             0                                     0                                 0
1898                                   0                             0                                     0                                 0
1518                                   0                             0                                     0                                 0
330                                    0                             0                                     0                                 0
1799                                   0                             0                                     0                                 0
     NameNew York Youth Jobs Program Tax Credit NameQETC Capital Tax Credit NameQETC Employment Credit
1422                                          0                           0                          0
1017                                          0                           0                          0
1860                                          0                           0                          0
679                                           0                           0                          0
129                                           0                           0                          0
930                                           0                           0                          0
1533                                          0                           0                          1
471                                           0                           0                          0
299                                           0                           0                          0
270                                           0                           0                          0
1211                                          0                           0                          0
1331                                          0                           0                          0
597                                           0                           0                          0
1301                                          0                           0                          0
1898                                          0                           0                          0
1518                                          0                           0                          0
330                                           1                           0                          0
1799                                          0                           0                          0
     NameQETC Facilities, Operations, and Training Credit NameReal Property Tax Relief Credit for Manufacturing
1422                                                    0                                                     0
1017                                                    0                                                     0
1860                                                    0                                                     0
679                                                     0                                                     0
129                                                     0                                                     1
930                                                     0                                                     0
1533                                                    0                                                     0
471                                                     0                                                     0
299                                                     0                                                     0
270                                                     0                                                     0
1211                                                    0                                                     0
1331                                                    0                                                     0
597                                                     0                                                     0
1301                                                    0                                                     0
1898                                                    0                                                     0
1518                                                    0                                                     0
330                                                     0                                                     0
1799                                                    0                                                     0
     NameSpecial Additional Mortgage Recording Tax Credit NameSTART-UP NY Tax Elimination Credit Group1,000,000 - 24,999,999 Group100,000 - 499,999
1422                                                    0                                      0                           0                      0
1017                                                    0                                      0                           0                      0
1860                                                    0                                      0                           0                      0
679                                                     0                                      0                           0                      0
129                                                     0                                      0                           0                      0
930                                                     0                                      1                           0                      0
1533                                                    0                                      0                           0                      0
471                                                     0                                      0                           0                      0
299                                                     0                                      0                           0                      0
270                                                     0                                      0                           0                      1
1211                                                    0                                      0                           0                      0
1331                                                    0                                      0                           0                      1
597                                                     0                                      0                           0                      0
1301                                                    0                                      0                           0                      0
1898                                                    0                                      0                           0                      0
1518                                                    0                                      0                           0                      1
330                                                     0                                      0                           1                      0
1799                                                    0                                      0                           0                      1
     Group100,000,000 - 499,999,999 Group25,000,000 - 49,999,999 Group50,000,000 - 99,999,999 Group500,000 - 999,999 Group500,000,000 - and over
1422                              0                            0                            0                      0                           0
1017                              1                            0                            0                      0                           0
1860                              0                            0                            0                      0                           1
679                               0                            0                            0                      1                           0
129                               0                            0                            0                      0                           0
930                               0                            0                            0                      0                           0
1533                              0                            0                            0                      0                           0
471                               0                            0                            0                      0                           0
299                               0                            0                            0                      0                           0
270                               0                            0                            0                      0                           0
1211                              0                            0                            1                      0                           0
1331                              0                            0                            0                      0                           0
597                               0                            0                            0                      0                           0
1301                              0                            0                            0                      0                           0
1898                              0                            0                            0                      1                           0
1518                              0                            0                            0                      0                           0
330                               0                            0                            0                      0                           0
1799                              0                            0                            0                      0                           0
     GroupZero or Net Loss         Num
1422                     1    3.000000
1017                     0    1.333333
1860                     0    4.000000
679                      0    3.000000
129                      0   69.000000
930                      1   16.000000
1533                     0    4.000000
471                      0   96.000000
299                      1    9.000000
270                      0    6.500000
1211                     0    1.666667
1331                     0   30.000000
597                      0    9.000000
1301                     1   25.000000
1898                     0   11.000000
1518                     0    1.000000
330                      0    7.000000
1799                     0   27.000000
 [ reached getOption("max.print") -- omitted 1518 rows ]

$y.train
   [1] 1.444633e+05 8.423750e+05 7.176375e+06 4.961167e+03 3.044377e+03 1.028000e+03 6.475250e+03 7.377635e+03 1.666888e+05 1.797438e+04 9.649170e+04
  [12] 1.531214e+05 1.689574e+06 9.546898e+05 6.607509e+04 3.853515e+05 1.631250e+05 8.420778e+03 1.076731e+04 4.837649e+05 2.425910e+04 1.081733e+04
  [23] 2.909133e+04 3.154922e+05 1.248333e+02 2.984333e+03 1.041887e+05 1.884164e+04 1.922213e+03 8.834333e+03 1.350001e+05 9.000000e+02 1.652030e+05
  [34] 2.317820e+06 9.014667e+03 7.734375e+04 2.668805e+03 1.291816e+06 1.445827e+05 1.198904e+05 4.806000e+03 1.598841e+05 2.381278e+05 1.291816e+06
  [45] 5.573088e+04 1.462504e+05 1.280000e+04 2.504000e+03 1.088920e+04 1.491991e+04 1.977783e+03 1.269140e+05 6.871308e+05 1.895283e+05 2.103778e+03
  [56] 1.088920e+04 3.328420e+06 1.077718e+06 2.966550e+05 2.697835e+07 8.956831e+06 5.188400e+04 1.638083e+05 2.461394e+03 6.726345e+05 2.682842e+05
  [67] 3.182500e+03 7.892796e+05 3.545919e+06 1.546916e+05 8.601000e+03 1.444793e+05 3.029539e+05 7.185038e+05 3.516372e+04 1.892595e+06 1.291639e+05
  [78] 3.596250e+05 4.224133e+04 1.062724e+06 4.986983e+04 1.277272e+03 2.817453e+04 4.616608e+05 7.099286e+03 2.005162e+05 1.119670e+05 9.076564e+02
  [89] 2.270700e+04 1.304214e+04 9.278836e+05 5.229374e+06 5.505667e+03 9.718222e+05 3.497500e+05 3.055396e+04 1.291816e+06 8.829722e+03 1.411650e+05
 [100] 1.520335e+05 2.350517e+05 2.662875e+04 2.984333e+03 2.317820e+06 2.317820e+06 3.170010e+05 3.853515e+05 8.561924e+03 4.025600e+04 9.820333e+03
 [111] 6.953466e+06 3.386785e+05 2.343167e+03 2.527122e+05 1.524894e+06 1.034997e+05 3.659458e+03 1.048103e+05 9.621489e+04 1.390581e+04 8.403113e+04
 [122] 1.498561e+05 7.709066e+05 6.233342e+04 5.459386e+04 6.988889e+04 2.361618e+04 1.511225e+05 2.909000e+03 1.396708e+05 6.955556e+02 6.510700e+04
 [133] 1.393300e+06 4.755113e+05 4.953022e+04 2.070642e+06 2.865400e+03 7.973200e+03 1.753420e+06 2.005981e+05 4.343602e+04 9.077196e+05 6.560525e+05
 [144] 2.718876e+05 2.573558e+05 4.640935e+05 4.088167e+03 1.907142e+05 8.431746e+05 8.334069e+02 4.711452e+06 2.437333e+03 5.206620e+05 1.365532e+06
 [155] 2.662875e+04 4.428599e+05 1.883396e+05 1.270637e+06 7.882333e+03 1.555957e+05 5.661475e+04 1.281247e+03 1.224495e+05 4.454760e+04 1.048040e+06
 [166] 1.414577e+07 2.551955e+05 4.000000e+03 2.935100e+04 1.089000e+03 7.850660e+02 1.208941e+03 1.017148e+05 8.430500e+04 8.166800e+03 7.785000e+04
 [177] 9.577243e+05 1.839021e+03 8.514848e+03 1.453340e+04 1.907825e+06 1.635961e+06 1.666667e+03 4.411375e+04 1.585990e+05 5.470139e+04 9.078692e+03
 [188] 2.057612e+06 5.963000e+03 3.881863e+07 1.097103e+05 2.875100e+04 1.259430e+05 1.419562e+04 3.533451e+06 3.568112e+04 8.183533e+04 9.277220e+04
 [199] 8.411148e+03 1.182098e+05 2.609570e+05 6.719991e+03 9.211780e+04 7.275000e+04 1.029659e+05 8.403640e+04 4.454760e+04 3.894155e+05 1.012616e+06
 [210] 2.875100e+04 2.875100e+04 6.953466e+06 2.049280e+04 8.088440e+04 6.387367e+02 1.528336e+04 4.986983e+04 3.514050e+05 1.457522e+05 1.797438e+04
 [221] 4.299765e+05 1.605500e+03 1.312732e+05 1.070463e+05 1.648964e+04 8.439882e+05 1.036925e+05 3.526312e+05 4.550158e+06 2.865085e+05 7.008638e+04
 [232] 1.604485e+06 3.867030e+05 5.951348e+03 1.006732e+05 1.342010e+05 1.593878e+04 3.172615e+03 2.243429e+04 6.666263e+05 6.574713e+06 2.257274e+05
 [243] 4.997866e+06 2.916333e+03 4.431619e+03 9.401431e+04 4.429659e+05 1.951614e+06 1.263178e+04 2.229875e+03 3.237500e+04 1.652056e+04 4.219450e+04
 [254] 7.237404e+04 3.599000e+03 8.034048e+04 1.350364e+05 1.981250e+03 8.297867e+04 1.361764e+04 1.550125e+05 1.883396e+05 2.019664e+03 9.895250e+03
 [265] 9.585714e+04 7.779916e+04 9.275383e+06 6.309391e+05 5.597556e+03 7.689884e+06 2.533744e+04 7.666998e+05 3.559825e+04 6.500000e+03 4.731587e+05
 [276] 2.043000e+03 3.599842e+06 1.723479e+05 5.659249e+05 2.701608e+04 1.531020e+03 7.022533e+04 1.442556e+05 9.195680e+04 2.917684e+06 4.104042e+05
 [287] 1.652030e+05 2.606807e+05 7.827581e+03 2.071826e+05 2.471333e+04 1.744272e+06 4.507765e+05 6.598476e+03 5.501250e+03 3.221225e+04 7.961263e+03
 [298] 1.431600e+05 1.195833e+05 2.486504e+05 1.744272e+06 9.639100e+04 3.249400e+03 4.724236e+04 3.463333e+02 2.743826e+05 1.395038e+07 4.000000e+03
 [309] 1.621466e+06 4.749600e+03 8.220014e+03 6.858830e+05 9.249500e+03 1.162711e+03 6.028500e+03 1.953371e+05 1.753420e+06 7.460362e+03 8.069371e+04
 [320] 2.065853e+03 1.308392e+04 6.116453e+04 9.479250e+03 1.768722e+03 4.409700e+04 7.164380e+05 1.839143e+03 2.052277e+06 8.500446e+04 2.387808e+05
 [331] 1.983803e+05 6.522300e+04 8.597294e+03 1.830973e+05 1.674600e+04 9.249500e+03 8.142886e+05 1.410010e+05 1.817167e+03 5.713889e+03 1.008445e+05
 [342] 1.509049e+05 1.336542e+05 2.174043e+04 2.881370e+05 1.316265e+05 1.776947e+04 1.017148e+05 5.720700e+04 2.363211e+03 8.035676e+06 3.352425e+04
 [353] 1.360056e+03 1.692011e+05 1.862500e+04 2.678972e+04 3.894155e+05 3.732190e+05 1.724660e+05 7.476289e+05 9.350000e+04 3.070124e+05 2.578891e+05
 [364] 2.427300e+04 5.057549e+02 7.893612e+05 1.442556e+05 2.388377e+05 1.961038e+03 4.336100e+03 6.522300e+04 2.952875e+04 3.894155e+05 1.254752e+05
 [375] 5.532592e+05 1.301051e+04 2.952875e+04 2.414375e+04 3.766700e+05 7.881465e+03 2.943000e+03 5.601905e+04 7.008638e+04 1.513386e+04 1.635961e+06
 [386] 6.517918e+05 1.000933e+05 1.577174e+06 3.203050e+04 8.834333e+03 2.797852e+05 3.759082e+05 7.911100e+04 9.140000e+04 2.046650e+05 1.724660e+05
 [397] 2.700000e+01 3.009937e+06 3.217702e+05 2.390226e+06 2.869385e+03 2.697835e+07 4.763629e+04 2.223962e+03 9.263605e+04 8.823204e+05 1.331250e+04
 [408] 1.580114e+05 3.106455e+03 3.599000e+03 7.528723e+05 5.516919e+03 4.206549e+06 7.385556e+02 6.596991e+04 3.784080e+04 6.866131e+04 2.159120e+05
 [419] 8.966268e+03 7.500000e+03 1.373150e+03 2.688150e+04 2.646539e+05 8.126870e+03 5.064518e+04 2.381278e+05 5.206620e+05 4.948418e+05 3.875917e+05
 [430] 1.364231e+05 2.070700e+04 2.249117e+04 1.631250e+04 1.430898e+03 2.874067e+04 1.112230e+06 5.055432e+04 5.690714e+03 8.069371e+04 3.661076e+02
 [441] 3.747375e+03 3.706131e+05 3.224383e+06 1.440787e+05 1.985550e+05 8.032067e+04 2.966550e+05 3.921104e+06 1.307548e+06 2.072544e+04 1.561672e+04
 [452] 4.184533e+04 4.290383e+04 3.475216e+06 2.682842e+05 9.649170e+04 5.238906e+03 8.673243e+03 8.410238e+05 3.512020e+05 9.275383e+06 4.629051e+05
 [463] 2.631080e+05 1.590391e+05 7.401750e+04 1.621466e+06 1.431961e+04 7.218750e+03 4.674235e+05 2.551955e+05 1.441000e+04 1.441926e+05 2.581267e+03
 [474] 1.201790e+05 2.692040e+05 2.931458e+05 1.264478e+05 1.553825e+06 3.955429e+03 6.159091e+04 1.821302e+05 3.867532e+05 1.272638e+05 3.506223e+04
 [485] 2.332435e+06 9.856200e+03 4.715981e+05 9.633245e+04 4.645433e+05 3.521641e+06 1.566158e+03 8.495484e+03 2.174043e+04 5.587362e+03 3.008432e+04
 [496] 8.475000e+04 7.388821e+05 2.551955e+05 8.295545e+03 6.500000e+03 9.625600e+03 9.643000e+03 7.218750e+03 2.600100e+04 9.087042e+04 2.038725e+04
 [507] 5.772857e+02 6.979000e+04 1.109067e+04 4.915443e+04 7.237286e+03 1.500000e+03 2.633555e+04 1.935780e+05 4.372832e+05 6.779667e+03 1.317561e+03
 [518] 3.723650e+04 8.329513e+05 1.399135e+06 1.115225e+04 4.735132e+04 1.782359e+04 4.867948e+05 4.233333e+04 5.698936e+05 1.033540e+04 2.060914e+04
 [529] 3.662863e+05 4.986983e+04 3.387741e+05 7.730148e+04 1.754811e+05 6.929400e+04 3.083700e+04 9.643000e+03 1.675607e+05 1.225665e+05 8.423750e+05
 [540] 2.174043e+04 8.834333e+03 6.382588e+05 1.537276e+04 1.358533e+04 2.966604e+05 1.797295e+03 2.934556e+03 4.767829e+03 1.945612e+05 1.525145e+05
 [551] 8.549525e+04 1.540060e+05 2.966550e+05 2.190692e+04 3.711855e+06 1.600392e+05 2.070700e+04 3.280333e+03 1.548511e+04 7.364275e+04 1.015137e+04
 [562] 4.288667e+03 7.218750e+03 1.767339e+05 1.524894e+06 4.276329e+03 1.593400e+03 1.674600e+04 3.627438e+05 1.860170e+05 6.330952e+02 9.055853e+05
 [573] 3.571560e+04 2.543800e+03 3.599842e+06 6.818975e+04 1.924658e+04 7.286300e+04 1.763107e+05 2.796945e+06 4.835950e+04 5.178571e+02 5.536867e+04
 [584] 1.010000e+04 6.505425e+06 6.871308e+05 1.378400e+05 3.264100e+04 9.552330e+05 7.547667e+03 2.966604e+05 1.719513e+04 6.675000e+03 5.268800e+04
 [595] 4.302760e+04 8.069371e+04 3.009937e+06 1.291816e+06 3.382220e+05 1.301195e+03 6.857040e+04 4.379652e+04 4.587867e+04 1.822071e+05 6.166634e+05
 [606] 1.891474e+05 6.567026e+05 1.958275e+04 4.589250e+05 6.807756e+02 4.837500e+04 5.666667e+03 5.690714e+03 4.281964e+05 6.590500e+06 9.174549e+03
 [617] 1.471271e+05 1.860649e+04 1.342010e+05 5.993612e+05 2.457747e+05 2.970000e+04 3.989468e+06 9.178216e+05 1.141380e+05 4.770928e+07 1.969696e+06
 [628] 3.370829e+04 1.035016e+05 1.263462e+04 4.559300e+03 5.032419e+03 1.900342e+04 8.980202e+03 6.644359e+04 2.309489e+06 5.354132e+05 7.596291e+05
 [639] 1.933758e+05 3.498428e+02 4.048120e+04 1.916667e+04 2.134563e+06 1.096976e+06 5.375000e+03 1.633797e+05 5.188400e+04 4.302778e+02 1.645415e+05
 [650] 5.149952e+05 4.454760e+04 9.482320e+05 7.282220e+04 4.339114e+04 3.311889e+06 4.172094e+05 6.040674e+02 3.647125e+05 1.322500e+05 3.956627e+05
 [661] 7.251105e+03 2.952875e+04 1.305160e+04 7.215350e+05 1.115700e+05 1.943908e+05 8.414412e+05 1.951614e+06 1.195486e+06 2.174291e+06 6.567026e+05
 [672] 1.815720e+04 1.020194e+06 4.459425e+04 2.658154e+05 2.185941e+04 7.148415e+05 3.989468e+06 7.264600e+03 3.258643e+04 1.263178e+04 9.000000e+03
 [683] 2.758867e+04 5.471792e+03 1.138104e+03 3.122021e+04 2.650302e+05 1.499504e+04 6.149972e+06 5.534600e+04 3.287828e+04 2.200770e+05 1.406547e+03
 [694] 2.062730e+06 1.077469e+06 2.535815e+04 1.811436e+04 1.462500e+04 1.297517e+05 5.762179e+03 3.712824e+04 1.792837e+05 2.086620e+04 3.816286e+02
 [705] 9.723300e+04 1.635961e+06 1.792837e+05 7.709066e+05 1.752400e+04 8.989200e+04 1.451944e+05 1.744272e+06 2.468480e+04 3.550520e+04 7.963766e+04
 [716] 7.714926e+04 1.085837e+03 1.642082e+06 6.004488e+05 1.631250e+04 8.631786e+03 4.375000e+03 9.000000e+02 2.494493e+06 3.931914e+04 1.951614e+06
 [727] 7.573100e+04 4.390320e+04 7.810820e+04 3.206332e+07 2.718876e+05 4.219450e+04 3.656250e+05 6.103333e+02 6.292798e+03 4.720975e+05 8.008404e+04
 [738] 2.093267e+04 5.204661e+04 6.747323e+07 2.633555e+04 1.107723e+06 1.075657e+04 1.666667e+03 2.352031e+05 1.682127e+03 1.066898e+04 4.551714e+03
 [749] 9.127015e+02 8.329513e+05 4.986983e+04 6.520600e+04 1.030300e+04 1.406217e+03 9.577243e+05 6.083896e+06 7.259900e+04 1.548711e+04 1.747579e+07
 [760] 3.730476e+04 4.341197e+05 2.317820e+06 1.883433e+06 9.150866e+04 2.257274e+05 4.614060e+03 7.218750e+03 1.844095e+04 9.090745e+04 8.088440e+04
 [771] 6.068333e+03 7.141463e+05 4.334150e+04 1.034446e+04 5.690714e+03 1.809172e+04 4.172444e+03 5.941159e+03 1.050744e+04 2.682842e+05 6.039756e+04
 [782] 3.282500e+03 4.299765e+05 2.857741e+06 1.115225e+04 3.387741e+05 2.399810e+06 9.479250e+03 1.835979e+06 1.246188e+04 1.845057e+05 6.209358e+06
 [793] 1.158932e+06 9.450000e+04 2.174043e+04 2.844688e+05 2.272808e+03 4.048120e+04 1.727830e+05 4.281964e+05 1.615562e+04 1.809172e+04 5.531483e+07
 [804] 1.264478e+05 4.139416e+05 2.056096e+04 1.280000e+04 9.249500e+03 3.009937e+06 1.593400e+03 5.603233e+04 1.389126e+05 4.891083e+04 3.084800e+04
 [815] 8.499895e+03 7.646458e+04 2.164482e+04 1.090874e+05 2.987667e+03 3.700803e+05 4.527100e+04 8.329513e+05 2.276824e+03 5.263393e+05 6.726345e+05
 [826] 1.546916e+05 1.113168e+04 2.693728e+04 1.220746e+06 2.427791e+06 5.206620e+05 4.010397e+06 3.672033e+04 6.500000e+03 5.382279e+05 5.109273e+03
 [837] 3.526312e+05 3.512020e+05 1.115549e+04 1.500000e+03 2.295050e+03 2.473152e+05 6.550323e+05 1.125441e+05 4.029300e+05 3.238555e+05 1.500000e+03
 [848] 1.621466e+06 1.253227e+05 4.198850e+04 2.381278e+05 1.935780e+05 6.818975e+04 1.440260e+06 4.202889e+04 2.010845e+06 4.436802e+06 2.771255e+05
 [859] 5.033900e+04 6.500000e+03 2.631080e+05 2.419256e+04 1.524894e+06 3.784080e+04 2.965254e+05 6.500000e+03 2.357709e+06 1.618973e+04 7.749743e+04
 [870] 9.997194e+04 2.527423e+05 3.445572e+06 3.974058e+05 5.881860e+05 3.075315e+05 7.709066e+05 1.783857e+03 7.747286e+04 1.226100e+05 2.089443e+04
 [881] 3.387257e+05 1.560272e+06 6.439684e+03 2.570000e+04 3.606750e+05 2.203167e+03 7.068560e+05 1.220746e+06 6.975000e+04 3.779488e+04 7.646000e+03
 [892] 7.541167e+03 5.125000e+03 2.262719e+06 1.938892e+04 2.692040e+05 6.140060e+04 1.792837e+05 4.402190e+05 1.575040e+04 7.090840e+04 3.337250e+05
 [903] 5.731001e+06 2.104515e+04 1.044764e+05 8.069371e+04 7.022533e+04 5.147775e+04 2.671048e+07 3.445871e+04 3.526312e+05 1.590991e+04 1.633174e+04
 [914] 4.837500e+04 1.883433e+06 3.735045e+04 7.220286e+03 8.345474e+03 2.875100e+04 8.380687e+05 1.577174e+06 4.048120e+04 3.919902e+05 7.893612e+05
 [925] 4.792659e+05 3.217702e+05 1.060600e+04 2.281777e+05 1.546333e+03 4.411375e+04 2.270700e+04 7.259900e+04 1.666667e+03 5.351866e+05 2.960200e+04
 [936] 1.171645e+04 2.070700e+04 1.247008e+06 1.933758e+05 1.309032e+06 3.021159e+05 2.768850e+04 2.633555e+04 1.809172e+04 2.127750e+05 4.110809e+05
 [947] 2.555815e+06 7.225000e+04 2.551955e+05 2.549870e+04 3.220990e+05 1.981250e+03 3.641286e+03 4.524049e+05 2.416150e+05 3.732190e+05 3.286906e+05
 [958] 3.963517e+05 2.049280e+04 2.534387e+04 9.779467e+04 6.861800e+04 2.593780e+04 2.579882e+05 9.113667e+03 1.196111e+06 4.248750e+05 5.599746e+02
 [969] 5.257556e+04 4.220304e+06 9.649170e+04 1.524894e+06 2.881370e+05 7.024000e+03 1.932345e+05 2.302996e+05 3.022333e+03 1.344000e+03 2.038725e+04
 [980] 2.909133e+04 8.755333e+03 7.850333e+03 4.967767e+04 2.689325e+03 1.453340e+04 3.059725e+04 1.103466e+05 5.650000e+04 8.000000e+03 4.986553e+04
 [991] 2.457591e+03 1.632398e+05 7.022533e+04 2.229369e+04 4.315057e+03 2.437333e+03 1.232106e+06 4.125917e+05 3.833333e+03 2.692040e+05
 [ reached getOption("max.print") -- omitted 536 entries ]

$X.test
     Year NameAlternative Fuels and Electric Vehicle Recharging Property Credit NameAlternative Minimum Tax Credit NameBeer Production Credit
2    2019                                                                     0                                  0                          0
6    2019                                                                     0                                  0                          0
10   2019                                                                     1                                  0                          0
12   2019                                                                     0                                  0                          0
25   2019                                                                     0                                  0                          0
26   2019                                                                     0                                  0                          0
28   2019                                                                     0                                  0                          0
30   2019                                                                     0                                  0                          0
32   2019                                                                     0                                  0                          0
35   2019                                                                     0                                  0                          0
38   2019                                                                     0                                  0                          0
50   2019                                                                     0                                  0                          0
53   2019                                                                     0                                  0                          0
54   2019                                                                     0                                  0                          0
63   2019                                                                     0                                  0                          0
70   2019                                                                     0                                  0                          0
76   2019                                                                     0                                  0                          0
85   2019                                                                     0                                  0                          0
     NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15
2                                                                                                0
6                                                                                                0
10                                                                                               0
12                                                                                               1
25                                                                                               0
26                                                                                               0
28                                                                                               0
30                                                                                               0
32                                                                                               0
35                                                                                               0
38                                                                                               0
50                                                                                               0
53                                                                                               0
54                                                                                               0
63                                                                                               0
70                                                                                               0
76                                                                                               0
85                                                                                               0
     NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15 NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08
2                                                                             0                                                                        0
6                                                                             0                                                                        0
10                                                                            0                                                                        0
12                                                                            0                                                                        0
25                                                                            0                                                                        0
26                                                                            0                                                                        0
28                                                                            0                                                                        0
30                                                                            0                                                                        0
32                                                                            0                                                                        0
35                                                                            0                                                                        0
38                                                                            0                                                                        0
50                                                                            0                                                                        0
53                                                                            0                                                                        0
54                                                                            0                                                                        0
63                                                                            0                                                                        0
70                                                                            0                                                                        0
76                                                                            0                                                                        0
85                                                                            0                                                                        0
     NameBrownfield Tax Credits - Remediation Real Property Tax Credit NameClean Heating Fuel Credit NameConservation Easement Tax Credit
2                                                                    0                             0                                    0
6                                                                    0                             0                                    0
10                                                                   0                             0                                    0
12                                                                   0                             0                                    0
25                                                                   1                             0                                    0
26                                                                   1                             0                                    0
28                                                                   1                             0                                    0
30                                                                   0                             1                                    0
32                                                                   0                             1                                    0
35                                                                   0                             0                                    1
38                                                                   0                             0                                    1
50                                                                   0                             0                                    0
53                                                                   0                             0                                    0
54                                                                   0                             0                                    0
63                                                                   0                             0                                    0
70                                                                   0                             0                                    0
76                                                                   0                             0                                    0
85                                                                   0                             0                                    0
     NameCredit for Employment of Persons with Disabilities NameCredit for Purchase of an Automated External Defibrillator
2                                                         0                                                              0
6                                                         0                                                              0
10                                                        0                                                              0
12                                                        0                                                              0
25                                                        0                                                              0
26                                                        0                                                              0
28                                                        0                                                              0
30                                                        0                                                              0
32                                                        0                                                              0
35                                                        0                                                              0
38                                                        0                                                              0
50                                                        0                                                              0
53                                                        0                                                              0
54                                                        0                                                              0
63                                                        0                                                              0
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25                                                           0                                 0                                                  0
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12                                              0                                                             0
25                                              0                                                             0
26                                              0                                                             0
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10                                                                                      0                                                   0
12                                                                                      0                                                   0
25                                                                                      0                                                   0
26                                                                                      0                                                   0
28                                                                                      0                                                   0
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35                                                                                      0                                                   0
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54                                                                                      0                                                   0
63                                                                                      0                                                   0
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76                                                                                      0                                                   0
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63                                                                            0                                   0                              0
70                                                                            0                                   0                              0
76                                                                            0                                   0                              0
85                                                                            0                                   0                              0
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2                            0                                             0                                                   0
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10                           0                                             0                                                   0
12                           0                                             0                                                   0
25                           0                                             0                                                   0
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63                           0                                             0                                                   0
70                           0                                             0                                                   0
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85                           0                                             0                                                   0
     NameInvestment Tax Credit NameInvestment Tax Credit for the Financial Services Industry NameLife Sciences Research & Development Tax Credit
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6                            0                                                             0                                                   0
10                           0                                                             0                                                   0
12                           0                                                             0                                                   0
25                           0                                                             0                                                   0
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63                           0                                                             0                                                   0
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76                           0                                                             0                                                   0
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6                                      0                             0                                     0                                 0
10                                     0                             0                                     0                                 0
12                                     0                             0                                     0                                 0
25                                     0                             0                                     0                                 0
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35                                     0                             0                                     0                                 0
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85                                     0                             0                                     0                                 0
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2                                             0                           0                          0
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10                                            0                           0                          0
12                                            0                           0                          0
25                                            0                           0                          0
26                                            0                           0                          0
28                                            0                           0                          0
30                                            0                           0                          0
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38                                            0                           0                          0
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54                                            0                           0                          0
63                                            0                           0                          0
70                                            0                           0                          0
76                                            0                           0                          0
85                                            0                           0                          0
     NameQETC Facilities, Operations, and Training Credit NameReal Property Tax Relief Credit for Manufacturing
2                                                       0                                                     0
6                                                       0                                                     0
10                                                      0                                                     0
12                                                      0                                                     0
25                                                      0                                                     0
26                                                      0                                                     0
28                                                      0                                                     0
30                                                      0                                                     0
32                                                      0                                                     0
35                                                      0                                                     0
38                                                      0                                                     0
50                                                      0                                                     0
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54                                                      0                                                     0
63                                                      0                                                     0
70                                                      0                                                     0
76                                                      0                                                     0
85                                                      0                                                     0
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2                                                       0                                      0                           0                      0
6                                                       0                                      0                           0                      0
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2                        0    3.000000
6                        0    1.000000
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28                       0    1.166667
30                       1  266.000000
32                       0   17.000000
35                       1    1.000000
38                       0    1.000000
50                       0    1.333333
53                       0    4.000000
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63                       0    4.000000
70                       0    1.428571
76                       1    9.000000
85                       0    3.000000
 [ reached getOption("max.print") -- omitted 367 rows ]

$y.test
  [1] 6.270533e+04 4.094677e+05 2.200770e+05 1.642082e+06 2.718876e+05 2.718876e+05 2.718876e+05 1.851951e+03 1.965588e+03 1.081733e+04 1.081733e+04
 [12] 9.350000e+04 9.852682e+05 9.852682e+05 2.479582e+05 9.275383e+06 1.382386e+07 8.166333e+04 7.521833e+03 2.025000e+04 1.007273e+05 4.288667e+03
 [23] 1.441000e+04 8.690525e+04 3.529140e+04 2.250933e+04 4.368017e+04 4.166496e+05 1.673048e+03 1.224760e+04 4.033988e+05 3.009937e+06 4.557862e+06
 [34] 4.436802e+06 4.436802e+06 1.951052e+05 1.951052e+05 1.951052e+05 1.787933e+03 8.000000e+03 8.000000e+03 1.666667e+04 4.000000e+03 6.979000e+04
 [45] 4.864249e+05 9.061236e+07 6.567026e+05 1.759552e+06 3.175900e+04 4.133590e+05 2.931458e+05 1.220746e+06 6.656878e+03 1.369802e+05 2.073250e+03
 [56] 3.282500e+03 3.723650e+04 4.621417e+04 5.147775e+04 5.147775e+04 1.855775e+04 1.806176e+05 4.334150e+04 1.883396e+05 2.134563e+06 9.031245e+05
 [67] 4.711452e+06 4.711452e+06 3.081000e+03 6.779667e+03 6.500000e+03 1.922176e+06 3.533451e+06 1.017148e+05 4.867948e+05 9.827525e+04 8.861392e+05
 [78] 2.233330e+06 1.980965e+05 7.893612e+05 7.384467e+04 2.122267e+04 4.305500e+04 1.724660e+05 8.312500e+03 1.960654e+05 1.895372e+05 1.860170e+05
 [89] 3.550520e+04 1.305918e+05 6.510700e+04 8.475000e+04 1.031893e+05 5.188400e+04 3.699730e+05 2.996425e+04 2.499283e+05 2.499283e+05 1.291816e+06
[100] 8.127092e+05 1.951614e+06 8.069371e+04 1.280000e+04 3.500000e+03 4.811593e+07 4.589250e+05 1.376282e+05 1.182098e+05 2.509321e+07 5.141760e+04
[111] 5.141760e+04 3.721344e+06 1.470486e+04 1.983803e+05 1.430607e+04 1.763827e+04 4.517570e+06 4.089729e+04 9.892656e+04 3.295417e+05 2.128814e+03
[122] 4.961167e+03 2.698137e+06 2.855810e+03 6.957592e+05 2.126993e+04 4.464000e+04 4.464000e+04 2.070700e+04 6.312500e+04 7.685714e+04 7.275000e+04
[133] 1.282233e+04 7.973200e+03 2.796945e+06 2.796945e+06 6.827385e+05 2.551955e+05 4.540254e+05 9.525000e+03 7.385556e+02 1.358533e+04 1.500000e+03
[144] 3.333333e+04 3.526312e+05 1.474218e+06 9.883970e+04 2.386651e+05 2.229698e+06 2.980568e+04 2.288953e+06 1.600152e+06 6.753602e+05 5.273845e+04
[155] 7.810820e+04 6.680000e+02 2.724733e+04 3.663453e+04 1.151319e+04 2.249117e+04 8.826000e+03 2.317820e+06 7.643536e+04 9.920675e+04 3.795877e+05
[166] 1.977606e+04 2.685822e+03 5.883905e+03 4.441692e+03 6.359594e+04 5.514430e+05 4.741105e+04 7.193025e+04 1.508482e+06 1.949050e+05 1.256800e+04
[177] 9.014667e+03 1.652667e+03 3.240708e+05 1.636045e+05 2.471333e+04 6.068333e+03 6.068333e+03 9.000000e+02 5.000000e+03 3.393300e+04 3.027754e+07
[188] 7.564780e+04 4.128836e+04 5.670456e+04 7.903272e+05 1.647877e+06 3.055000e+04 8.423750e+05 1.090874e+05 5.378571e+02 5.922277e+05 1.030300e+04
[199] 1.030300e+04 7.008638e+04 8.010614e+06 5.874554e+04 4.891083e+04 2.551117e+04 4.063938e+03 6.703886e+04 7.177040e+04 3.691667e+04 1.589467e+04
[210] 5.795531e+05 1.384138e+04 2.983178e+05 2.181643e+05 2.181643e+05 8.051457e+05 2.916333e+03 2.916333e+03 8.333333e+02 8.050171e+04 2.341759e+06
[221] 1.389300e+04 1.713608e+05 4.281964e+05 4.281964e+05 4.230000e+05 9.592945e+04 3.683733e+05 5.060070e+04 1.954157e+05 5.990749e+04 5.321884e+05
[232] 9.649170e+04 1.147545e+04 1.756816e+04 2.333804e+05 3.212752e+06 1.815720e+04 1.574442e+03 1.585990e+05 1.585990e+05 7.039875e+03 1.817167e+03
[243] 1.817167e+03 2.631080e+05 1.289623e+04 6.081111e+03 3.878656e+05 2.794458e+05 4.938133e+04 3.230000e+02 5.501250e+03 1.000000e+03 2.150442e+06
[254] 8.666300e+04 2.096018e+06 1.358255e+05 3.224167e+05 3.778690e+04 5.412605e+05 5.962975e+04 1.917436e+04 4.290383e+04 4.290383e+04 1.040245e+04
[265] 1.753420e+06 1.498433e+05 7.791730e+04 1.792837e+05 1.611846e+03 2.671333e+03 3.334000e+03 6.916667e+03 1.546916e+05 2.985750e+04 2.985750e+04
[276] 3.387741e+05 2.966550e+05 1.349429e+03 7.541167e+03 8.333333e+02 1.010000e+04 1.010000e+04 3.784080e+04 5.916069e+05 2.844688e+05 3.728435e+05
[287] 4.763364e+05 7.853154e+05 4.732412e+05 8.977273e+02 1.459739e+05 3.917140e+05 1.365532e+06 2.915842e+04 2.545867e+03 6.675000e+03 1.722175e+04
[298] 1.943908e+05 1.280000e+04 3.376638e+04 1.113726e+04 2.633555e+04 2.633555e+04 1.021064e+05 3.337250e+05 1.081118e+05 2.625417e+05 1.027671e+05
[309] 7.064006e+04 5.689091e+05 8.933342e+04 2.871402e+02 2.261608e+06 1.386061e+05 1.708555e+04 7.812500e+04 7.760417e+04 1.885399e+04 4.555419e+05
[320] 1.936990e+05 8.720815e+04 4.926557e+05 1.508330e+05 3.732776e+05 1.915909e+05 2.266036e+04 6.687111e+04 3.218191e+05 1.345040e+06 7.565226e+02
[331] 8.422389e+05 1.752836e+04 2.224450e+05 1.359291e+05 2.777950e+04 1.545613e+05 3.869246e+05 3.329819e+04 2.464650e+05 5.268800e+04 1.926750e+04
[342] 5.268800e+04 1.532851e+04 1.761740e+05 2.385813e+05 2.343167e+03 8.239147e+04 1.094581e+05 1.978800e+05 2.772085e+03 1.410062e+04 1.104294e+04
[353] 1.374426e+04 2.240877e+05 2.792584e+03 4.481963e+04 5.703256e+05 1.823070e+05 3.808170e+05 2.901302e+07 6.624115e+04 3.456612e+04 6.230926e+02
[364] 2.262116e+05 1.965676e+05 2.200508e+05 1.833129e+06 2.837499e+03 5.828539e+02 4.791057e+07 3.064511e+04 2.634839e+05 1.531092e+04 4.959974e+03
[375] 5.110326e+05 3.635190e+03 5.675850e+04 4.368009e+05 1.648528e+07 4.285965e+04 1.161933e+04 3.644922e+05 9.586857e+03 5.011701e+05 2.681130e+06

$data.train

$data.test
NA

Lasso regression for comparison to Forward Stepwise

# calc_MSE <- function (model, x.test, y.test){
#   y.predict <- predict(model, newdata = x.test)
#   return(mean((y.predict - y.test)^2))
# }

xy.splits <- list('income' = income.data.split, 
                  'industry' = industry.data.split, 
                  'income.sat' = income.data.split.sat, 
                  'industry.sat' = industry.data.split.sat)

lasso.list <- c('income', 'industry', 'income.sat', 'industry.sat')
baseline.list <- c('income.sat', 'industry.sat', 'income.sat', 'industry.sat')
ridge.alpha <- 0

for (a in 1:4){
  i = lasso.list[a]
  b = baseline.list[a]
  X.train <- xy.splits[[i]][['X.train']]
  y.train <- xy.splits[[i]][['y.train']]
  X.test <- xy.splits[[i]][['X.test']]
  y.test <- xy.splits[[i]][['y.test']]
  X.test.sat <- xy.splits[[b]][['X.test']]
  y.test.sat <- xy.splits[[b]][['y.test']]
  data.train <- xy.splits[[i]][['data.train']]
  data.test <- xy.splits[[i]][['data.test']]
  
  #create lambda grid
  lambda.grid = 10^seq(2, -5, length = 100)
  
  #create lasso models with lambda.grid
  lasso.models = glmnet(X.train, y.train, alpha = ridge.alpha, lambda = lambda.grid)
  
  #visualize coefficient shrinkage
  plot(lasso.models, xvar = "lambda", label = TRUE, main = paste("Lasso Regression:", i))
  
  #Cross Validation to find best lambda
  set.seed(0)
  cv.lasso.models <- cv.glmnet(X.train, y.train, alpha = ridge.alpha, lambda = lambda.grid, nfolds = 10)
  
  #visualize cross validation for lambda that minimizes the mean squared error.
  plot(cv.lasso.models, main = paste("Lasso Regression:", i))
  
  #Checking the best lambda
  log(cv.lasso.models$lambda.min)
  best.lambda <- cv.lasso.models$lambda.min
  print(paste(i, ' best.lambda:', best.lambda))
  # best lambda with all the variables was found to be 0.0006892612
  # best lambda with only the bwdBIC coefficients included was found to be 0.0003053856
  
  #looking at the lasso coefficients for the best.lambda
  best.lambda.coeff <- predict(lasso.models, s = best.lambda, type = "coefficients")
  print('Number of Coefficients:')
  print(dim(best.lambda.coeff)[1])
  
  #fitting a model with the best lambda found to be 0.000689 and using it to make predictions for the testing data.
  lasso.best.lambda.train.pred <- predict(lasso.models, s = best.lambda, newx = X.test)
  lasso.best.lambda.train.pred
  
  #checking MSE
  MSE.lasso <- mean((lasso.best.lambda.train.pred - y.test)^2)
  sat.model.bc <- lm(Avg.bc ~., data = data.train)
  
  
  temp.df <- as.data.frame(X.test.sat) #temp fix
  colnames(temp.df) <- str_replace_all(colnames(temp.df), "[`]", '')
  
  y.predict <- predict(sat.model.bc, newdata = temp.df)
  MSE.sat <- mean((y.predict - y.test.sat)^2)
  
  print(paste(i, ' Lasso MSE: ', MSE.lasso, ' ', b, ' Saturated MSE: ', MSE.sat))

  metrics <- eval_results(y.test, lasso.best.lambda.train.pred, data.test)
  print(metrics)
  print('********************************')
}

Function to show metrics (R^2 and MSE) for Regularization (Ridge/Lasso)

#all.dfs <- list(income_cleaned, income_cleaned_bc, income.dummy.bc)

formulas <- list(income_cleaned = sat.formula, 
                 income_cleaned_bc = sat.formula.bc, 
                 income.data.split.sat = sat.formula.bc, 
                 income.data.split.best = income.best.formula,
                 industry_cleaned = sat.formula, 
                 industry_cleaned_bc = sat.formula.bc, 
                 industry.data.split.sat = sat.formula.bc, 
                 industry.data.split.best = industry.best.formula)

all.splits <- list(
  'income_cleaned' = test_train_split(income_cleaned, formulas[['income_cleaned']]),
  'income_cleaned_bc' = test_train_split(income_cleaned_bc, formulas[['income_cleaned_bc']]),
  'income.data.split.sat' = test_train_split(income.dummy.bc, formulas[['income.data.split.sat']]),
  'income.data.split.best' = test_train_split(income.dummy.bc, formulas[['income.data.split.best']]),
  'industry_cleaned' = test_train_split(industry_cleaned, formulas[['industry_cleaned']]),
  'industry_cleaned_bc' = test_train_split(industry_cleaned_bc, formulas[['industry_cleaned_bc']]),
  'industry.data.split.sat' = test_train_split(industry.dummy.bc, formulas[['industry.data.split.sat']]),
  'industry.data.split.best' = test_train_split(industry.dummy.bc, formulas[['industry.data.split.best']])
)

#For loops initialization
no.reg.r2 <- c() 
lasso.reg.r2 <- c()
ridge.reg.r2 <- c()


for (i in names(all.splits)) {
  #no regularization
  m = lm(formulas[[i]], all.splits[[i]][['data.train']])
  #no.reg.r2 <- c(no.reg.r2, summary(m)$adj.r.squared)
  y.predict = predict(m, newdata = as.data.frame(all.splits[[i]][['X.test']]))
  adj.R2 <- eval_results(all.splits[[i]][['y.test']], y.predict, all.splits[[i]][['data.test']], length(coef(m)))['Rsquare']
  no.reg.r2 <- c(no.reg.r2, adj.R2)
  
  #lasso regularization
  lasso.reg.r2 <- c(lasso.reg.r2, regularization_func(all.splits[[i]], 1, i))
  
  #ridge regularization
  ridge.reg.r2 <- c(ridge.reg.r2, regularization_func(all.splits[[i]], 0, i))
}
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df.rsquare <- as.data.frame(cbind('noReg' = no.reg.r2, 'lassoReg' = lasso.reg.r2, 'ridgeReg' = ridge.reg.r2))
rownames(df.rsquare) = names(all.splits)
df.rsquare
# sat.model.bc <- lm(Avg.bc ~., data = xy.splits.sat[['industry']][['data.train']])
# 
# temp.df <- as.data.frame(xy.splits.sat[['industry']][['X.test']])
# 
# colnames(temp.df)[57]
# 
# colnames(temp.df) <- str_replace_all(colnames(temp.df), "[`]", '')
# colnames(temp.df)
# 
# y.predict <- predict(sat.model.bc, newdata = temp.df)
# MSE.sat <- mean((y.predict - xy.splits.sat[['industry']][['y.test']])^2)
# 
# print(paste(i, ' Lasso MSE: ', MSE.lasso, ' Saturated MSE: ', MSE.sat))
# 
# summary(sat.model.bc)$coefficients
# as.data.frame(xy.splits.sat[['industry']][['X.test']]) %>% select(starts_with('`GroupOth'))
# Compute R^2 from true and predicted values
eval_results <- function(true, predicted, df, p) {
  n = nrow(df)
  adj.RSS <- sum((predicted - true)^2)/(n-p-1)
  adj.TSS <- sum((true - mean(true))^2)/(n-1)
  adj.R_square <- 1 - adj.RSS / adj.TSS
  #RMSE = sqrt(RSS/n)
  
  return(c(Rsquare = R_square))
}

#formula for adjusted R^2 found in following link.
#https://www.graphpad.com/guides/prism/latest/curve-fitting/reg_adjusted-r-squared.htm
as.data.frame(lasso.best.lambda.train.pred) %>% mutate(Avg_in_dollars = (lasso.best.lambda.train.pred*lambda.bc+1)^(1/lambda.bc))
calc_MSE(sat.model.bc, as.data.frame(income.sat.data.split[['X.test']]), income.sat.data.split[['y.test']])
[1] 1.473686
---
title: "R Notebook"
output: html_notebook
---
Call Libraries
```{r} 
library(tidyverse)
library(caret)
library(MASS)
library(car)
library(moments)
```


Calling the Transformed Datasets
```{r}
income_cleaned = read_csv('NYS_Corp_Tax_Credit_data/income_cleaned.csv')
income_cleaned = income_cleaned %>% select(-Amount)

industry_cleaned = read_csv('NYS_Corp_Tax_Credit_data/industry_cleaned.csv')
industry_cleaned = industry_cleaned %>% select(-Amount)
```


Creating the Models
```{r}
sat.model.summary <- function (df, field, sat.formula){
    
    #Shapiro-Wilks test to evaluate normality
    print(shapiro.test(df[[field]]))
    
    #Kurtosis evaluation (normal distribution has a value close to 3)
    print('kurtosis')
    print(kurtosis(df[[field]]))
    linear.model.cleaned = lm(sat.formula, data = df)
    print(summary(linear.model.cleaned))
    plot(linear.model.cleaned)
    
    #histograms of response variable to check distribution
    print(df %>% 
      ggplot(aes_string(field)) + 
      geom_histogram() + 
      labs(title = 'Average Credit Amount Distribution') + 
      theme(plot.title = element_text(hjust = 0.5)))
    
    #Checking multicollinearity using VIF measurement
    print(vif(linear.model.cleaned))
    influencePlot(linear.model.cleaned)
    #avPlots(linear.model.cleaned)
}


sat.formula <- Avg ~ .
sat.field <- 'Avg'

sat.model.summary(income_cleaned, sat.field, sat.formula)
income.model <- lm(sat.formula, data = income_cleaned)


sat.model.summary(industry_cleaned, sat.field, sat.formula)
industry.model <- lm(sat.formula, data = industry_cleaned)
```

Correcting violation of Normality in previous model with BoxCox transform
```{r}
bc_func <- function (lm.cleaned, lambda.range){
  bc = boxCox(lm.cleaned, lambda = lambda.range)
  #Extracting the best lambda value.
  return(bc$x[which(bc$y == max(bc$y))])
}
  
#Income Group Dataset
income.lambda.bc = bc_func(income.model, seq(-0.2, 0.2, 1/10))
income.lambda.bc

#Industry Group Dataset
industry.lambda.bc = bc_func(industry.model, seq(-0.2, 0.2, 1/10))
industry.lambda.bc

bc_transform <- function(df, lambda.bc){
  return (df %>% 
            mutate(Avg.bc = (Avg^lambda.bc -1)/lambda.bc) %>% 
            select(-c(Avg))) #took out field Amount
}

#Income Group Dataset
income_cleaned_bc <- bc_transform(income_cleaned, income.lambda.bc)
income.model.bc = lm(Avg.bc ~ ., data = income_cleaned_bc)

#Industry Group Dataset
industry_cleaned_bc <- bc_transform(industry_cleaned, industry.lambda.bc)
industry.model.bc = lm(Avg.bc ~ ., data = industry_cleaned_bc)
```

Checking linear regression assumptions for the transformed data.
```{r}
sat.formula.bc <- Avg.bc ~ .
sat.field.bc <- 'Avg.bc'

#Income
sat.model.summary(income_cleaned_bc, sat.field.bc, sat.formula.bc)

#Industry
sat.model.summary(industry_cleaned_bc, sat.field.bc, sat.formula.bc)
```

BIC comparison before and after BoxCox transform
```{r}
BIC(income.model.bc, income.model)
BIC(industry.model.bc, industry.model)
```

Stepwise Regression on Income_cat_bc (boxcox transformed dataset)
```{r}
#creating dummy variable columns for stepwise
dummy_func <- function (df){
  x = model.matrix(Avg.bc ~., df)[, -1]
  dummy_bc = as.data.frame(x) %>% mutate(Avg.bc = df$Avg.bc)
  #colnames(dummy_bc) <- str_replace_all(colnames(dummy_bc), "-|'|/| |,|�|&" , '_')
  colnames(dummy_bc) <- str_replace_all(colnames(dummy_bc), "[-'/ ,�&()`]" , '_')
  return(dummy_bc)
}
```

Cleaning column names further so stepwise regression doesn't present any errors
```{r}
#Income Group Dataset
income.dummy.bc <- dummy_func(income_cleaned_bc)
#colnames(income.dummy.bc)[37] <- 'NameManufactureru0092s_Real_Property_Tax_Credit'
colnames(income.dummy.bc)

#Industry Group Dataset
industry.dummy.bc <- dummy_func(industry_cleaned_bc)
#colnames(industry.dummy.bc)[35] <- 'NameManufactureru0092s_Real_Property_Tax_Credit'
colnames(industry.dummy.bc)
```

Stepwise regression using BIC as the criteria (k = log(n)).
```{r}
#Creating Stepwise Models
bcs = list(income = income.dummy.bc, industry = industry.dummy.bc)
model.fulls = list(income = lm(Avg.bc ~ ., data = income.dummy.bc), industry = lm(Avg.bc ~ ., data = industry.dummy.bc)) #All variables
model.emptys = list(income = lm(Avg.bc ~ 1, data = income.dummy.bc), industry = lm(Avg.bc ~ 1, data = industry.dummy.bc)) #intercept only
k = c('income', 'industry')
forwardBIC = list(income = NULL, industry = NULL)
backwardBIC = list(income = NULL, industry = NULL)

for (i in k){
  bc = bcs[[i]]
  scope = list(lower = formula(model.emptys[[i]]), upper = formula(model.fulls[[i]]))
  n_obs = bc %>% count() %>% dplyr::first()
  forwardBIC[[i]] = step(model.emptys[[i]], scope, direction = "forward", k = log(n_obs))
  backwardBIC[[i]] = step(model.fulls[[i]], scope, direction = "backward", k = log(n_obs))
}
```

Selecting Best Formula per Dataset from Stepwise Regressions
```{r}
bic_func <- function (BIC.model){
  print('Adjusted R Squared:')
  print(summary(BIC.model)$adj.r.squared)
  print('Number of Coefficients:')
  print(dim(summary(BIC.model)$coefficient)[1])
  print('VIF Check: ')
  print(max(vif(BIC.model)))
  print("*************************")
}

bic_func(forwardBIC[['income']])
bic_func(backwardBIC[['income']])
bic_func(forwardBIC[['industry']]) 
bic_func(backwardBIC[['industry']])



#Manual reduction of variables using VIF and then checked versus saturated model with Anova. This was not used because the saturated model contained multicollinearity issues as indicated by a high VIF score on some coefficients. And the anova test suggested that the coefficients removed in the reduced model were informative in our model, so we couldn't use it either. Thus Stepwise reduction is the preferred method for best model fit.

# VIF.variables <- as.data.frame(vif(model.fulls[['industry']])) %>% 
#   select(VIF = `vif(model.fulls[["industry"]])`) %>% 
#   filter(VIF > 5) %>% rownames()
# 
# industry.dummy.bc.VIF <- industry.dummy.bc %>% select(-all_of(VIF.variables))
# industry.model.VIF <- lm(Avg.bc ~ ., data = industry.dummy.bc.VIF)
# summary(industry.model.VIF)
# anova(industry.model.VIF, model.fulls[['industry']])

```

Best Model Selection from Stepwise
```{r}
#The Best Models selected for both income and industry were forwardBIC.

#Income Group Dataset
income.best.formula <- forwardBIC[['income']]$call[[2]]
income.best.formula

#Industry Group Dataset
industry.best.formula <- forwardBIC[['industry']]$call[[2]]
industry.best.formula
```


Splitting data up into test data and training data (test data is for year 2019, training is the rest)
```{r}
test_train_split <- function(dummy_bc, best.formula) {
  # data.test <- dummy_bc %>% filter(Year == 2019)
  # data.train <- dummy_bc %>% filter(Year != 2019)
  X <- model.matrix(best.formula, data = dummy_bc)[,-1]
  y <- as.matrix(dummy_bc %>% select(all.vars(best.formula)[1]))
  
  set.seed(0)
  train.i = sample(1:nrow(dummy_bc), 0.8*nrow(dummy_bc), replace = F)
  
  #train
  X.train <- X[train.i,]
  y.train <- y[train.i,]
  
  #test
  X.test <- X[-train.i,]
  y.test <- y[-train.i,]
  
  data.train <- as.data.frame(cbind(y.train, X.train))
  data.test <- as.data.frame(cbind(y.test, X.test))
  colnames(data.train)[1] = all.vars(best.formula)[1]
  colnames(data.test)[1] = all.vars(best.formula)[1]
  
  return (list('X.train' = X.train, 'y.train' = y.train, 'X.test' = X.test, 'y.test' = y.test, 'data.train' = data.train, 'data.test' = data.test))
}
```

```{r}
test_train_split_old <- function(dummy_bc, best.formula) {
  # data.test <- dummy_bc %>% filter(Year == 2019)
  # data.train <- dummy_bc %>% filter(Year != 2019)
  set.seed(0)
  train.i = sample(1:nrow(dummy_bc), 0.8*nrow(dummy_bc), replace = F)
  data.train <- dummy_bc %>% slice(train.i)
  data.test <- dummy_bc %>% slice(-train.i)
  
  #train
  #X.train <- as.matrix(data.train %>% select(-Avg.bc))
  X.train <- model.matrix(best.formula, data = data.train)[,-1]
  y.train <- as.matrix(data.train %>% select(all.vars(best.formula)[1]))

  #test
  #X.test <- as.matrix(data.test %>% select(-Avg.bc))
  X.test <- model.matrix(best.formula, data = data.test)[,-1]
  y.test <- as.matrix(data.test %>% select(all.vars(best.formula)[1]))
  
  #return (list('X.train' = X.train, 'y.train' = y.train, 'X.test' = X.test, 'y.test' = y.test, 'data.train' = data.train, 'data.test' = data.test))
}

#Income
income.data.split.sat <- test_train_split(income.dummy.bc, Avg.bc ~ .)
income.data.split <- test_train_split(income.dummy.bc, income.best.formula)

#Industry
industry.data.split.sat <- test_train_split(industry.dummy.bc, Avg.bc ~ .)
industry.data.split <- test_train_split(industry.dummy.bc, industry.best.formula)

test_train_split(income_cleaned, sat.formula)

```


Lasso regression for comparison to Forward Stepwise
```{r}
# calc_MSE <- function (model, x.test, y.test){
#   y.predict <- predict(model, newdata = x.test)
#   return(mean((y.predict - y.test)^2))
# }

xy.splits <- list('income' = income.data.split, 
                  'industry' = industry.data.split, 
                  'income.sat' = income.data.split.sat, 
                  'industry.sat' = industry.data.split.sat)

lasso.list <- c('income', 'industry', 'income.sat', 'industry.sat')
baseline.list <- c('income.sat', 'industry.sat', 'income.sat', 'industry.sat')
ridge.alpha <- 0

for (a in 1:4){
  i = lasso.list[a]
  b = baseline.list[a]
  X.train <- xy.splits[[i]][['X.train']]
  y.train <- xy.splits[[i]][['y.train']]
  X.test <- xy.splits[[i]][['X.test']]
  y.test <- xy.splits[[i]][['y.test']]
  X.test.sat <- xy.splits[[b]][['X.test']]
  y.test.sat <- xy.splits[[b]][['y.test']]
  data.train <- xy.splits[[i]][['data.train']]
  data.test <- xy.splits[[i]][['data.test']]
  
  #create lambda grid
  lambda.grid = 10^seq(2, -5, length = 100)
  
  #create lasso models with lambda.grid
  lasso.models = glmnet(X.train, y.train, alpha = ridge.alpha, lambda = lambda.grid)
  
  #visualize coefficient shrinkage
  plot(lasso.models, xvar = "lambda", label = TRUE, main = paste("Lasso Regression:", i))
  
  #Cross Validation to find best lambda
  set.seed(0)
  cv.lasso.models <- cv.glmnet(X.train, y.train, alpha = ridge.alpha, lambda = lambda.grid, nfolds = 10)
  
  #visualize cross validation for lambda that minimizes the mean squared error.
  plot(cv.lasso.models, main = paste("Lasso Regression:", i))
  
  #Checking the best lambda
  log(cv.lasso.models$lambda.min)
  best.lambda <- cv.lasso.models$lambda.min
  print(paste(i, ' best.lambda:', best.lambda))
  # best lambda with all the variables was found to be 0.0006892612
  # best lambda with only the bwdBIC coefficients included was found to be 0.0003053856
  
  #looking at the lasso coefficients for the best.lambda
  best.lambda.coeff <- predict(lasso.models, s = best.lambda, type = "coefficients")
  print('Number of Coefficients:')
  print(dim(best.lambda.coeff)[1])
  
  #fitting a model with the best lambda found to be 0.000689 and using it to make predictions for the testing data.
  lasso.best.lambda.train.pred <- predict(lasso.models, s = best.lambda, newx = X.test)
  lasso.best.lambda.train.pred
  
  #checking MSE
  MSE.lasso <- mean((lasso.best.lambda.train.pred - y.test)^2)
  sat.model.bc <- lm(Avg.bc ~., data = data.train)
  
  
  temp.df <- as.data.frame(X.test.sat) #temp fix
  colnames(temp.df) <- str_replace_all(colnames(temp.df), "[`]", '')
  
  y.predict <- predict(sat.model.bc, newdata = temp.df)
  MSE.sat <- mean((y.predict - y.test.sat)^2)
  
  print(paste(i, ' Lasso MSE: ', MSE.lasso, ' ', b, ' Saturated MSE: ', MSE.sat))

  metrics <- eval_results(y.test, lasso.best.lambda.train.pred, data.test)
  print(metrics)
  print('********************************')
}
```

Function to show metrics (R^2 and MSE) for Regularization (Ridge/Lasso)
```{r}
regularization_func <- function (data, alpha, name){
  X.train <- data[['X.train']]
  y.train <- data[['y.train']]
  X.test <- data [['X.test']]
  y.test <- data[['y.test']]
  data.test <- data[['data.test']]
  # print(colnames(X.train))
  # print(colnames(X.test))
  # print(setdiff(colnames(X.train), colnames(X.test)))
  
  #create lambda grid
  lambda.grid = 10^seq(10, -10, length = 100)
  
  #create lasso models with lambda.grid
  lasso.models = glmnet(X.train, y.train, alpha = ridge.alpha, lambda = lambda.grid)
  
  #visualize coefficient shrinkage
  # plot(lasso.models, xvar = "lambda", label = TRUE, main = paste("Lasso Regression:", i))
  
  #Cross Validation to find best lambda
  set.seed(0)
  cv.lasso.models <- cv.glmnet(X.train, y.train, alpha = ridge.alpha, lambda = lambda.grid, nfolds = 10)
  
  #visualize cross validation for lambda that minimizes the mean squared error.
  plot(cv.lasso.models, main = paste("Alpha:", alpha, "Regression:", name))
  
  #Checking the best lambda
  # log(cv.lasso.models$lambda.min)
  # best.lambda <- cv.lasso.models$lambda.min
  # print(paste(i, ' best.lambda:', best.lambda))
  # best lambda with all the variables was found to be 0.0006892612
  # best lambda with only the bwdBIC coefficients included was found to be 0.0003053856
  
  #looking at the lasso coefficients for the best.lambda
  # best.lambda.coeff <- predict(lasso.models, s = cv.lasso.models$lambda.min, type = "coefficients")
  # print('Number of Coefficients:')
  # print(dim(best.lambda.coeff)[1])
  
  #fitting a model with the best lambda found to be 0.000689 and using it to make predictions for the testing data.
  lasso.best.lambda.train.pred <- predict(lasso.models, s = cv.lasso.models$lambda.min, newx = X.test)
  lasso.best.lambda.train.pred
  
  
  #checking MSE
  MSE.lasso <- mean((lasso.best.lambda.train.pred - y.test)^2)
  print(paste('Dimensions of the Alpha:', alpha, ' Regression Coefficients for:', name))
  print(dim(coef(lasso.models))[1])
  p = dim(coef(lasso.models))[1]
  return(eval_results(y.test, lasso.best.lambda.train.pred, data.test, p)['Rsquare'])
}

regularization_func(all.splits[['income_cleaned']], 0, 'income_cleaned')
regularization_func(all.splits[['income_cleaned_bc']], 0, 'income_cleaned_bc')
regularization_func(all.splits[['income.data.split.sat']], 0, 'income.data.split.sat')
```


```{r}
#all.dfs <- list(income_cleaned, income_cleaned_bc, income.dummy.bc)

formulas <- list(income_cleaned = sat.formula, 
                 income_cleaned_bc = sat.formula.bc, 
                 income.data.split.sat = sat.formula.bc, 
                 income.data.split.best = income.best.formula,
                 industry_cleaned = sat.formula, 
                 industry_cleaned_bc = sat.formula.bc, 
                 industry.data.split.sat = sat.formula.bc, 
                 industry.data.split.best = industry.best.formula)

all.splits <- list(
  'income_cleaned' = test_train_split(income_cleaned, formulas[['income_cleaned']]),
  'income_cleaned_bc' = test_train_split(income_cleaned_bc, formulas[['income_cleaned_bc']]),
  'income.data.split.sat' = test_train_split(income.dummy.bc, formulas[['income.data.split.sat']]),
  'income.data.split.best' = test_train_split(income.dummy.bc, formulas[['income.data.split.best']]),
  'industry_cleaned' = test_train_split(industry_cleaned, formulas[['industry_cleaned']]),
  'industry_cleaned_bc' = test_train_split(industry_cleaned_bc, formulas[['industry_cleaned_bc']]),
  'industry.data.split.sat' = test_train_split(industry.dummy.bc, formulas[['industry.data.split.sat']]),
  'industry.data.split.best' = test_train_split(industry.dummy.bc, formulas[['industry.data.split.best']])
)

#For loops initialization
no.reg.r2 <- c() 
lasso.reg.r2 <- c()
ridge.reg.r2 <- c()


for (i in names(all.splits)) {
  #no regularization
  m = lm(formulas[[i]], all.splits[[i]][['data.train']])
  #no.reg.r2 <- c(no.reg.r2, summary(m)$adj.r.squared)
  y.predict = predict(m, newdata = as.data.frame(all.splits[[i]][['X.test']]))
  adj.R2 <- eval_results(all.splits[[i]][['y.test']], y.predict, all.splits[[i]][['data.test']], length(coef(m)))['Rsquare']
  no.reg.r2 <- c(no.reg.r2, adj.R2)
  
  #lasso regularization
  lasso.reg.r2 <- c(lasso.reg.r2, regularization_func(all.splits[[i]], 1, i))
  
  #ridge regularization
  ridge.reg.r2 <- c(ridge.reg.r2, regularization_func(all.splits[[i]], 0, i))
}

```


```{r}
df.rsquare <- as.data.frame(cbind('noReg' = no.reg.r2, 'lassoReg' = lasso.reg.r2, 'ridgeReg' = ridge.reg.r2))
rownames(df.rsquare) = names(all.splits)
df.rsquare
```


```{r}
# sat.model.bc <- lm(Avg.bc ~., data = xy.splits.sat[['industry']][['data.train']])
# 
# temp.df <- as.data.frame(xy.splits.sat[['industry']][['X.test']])
# 
# colnames(temp.df)[57]
# 
# colnames(temp.df) <- str_replace_all(colnames(temp.df), "[`]", '')
# colnames(temp.df)
# 
# y.predict <- predict(sat.model.bc, newdata = temp.df)
# MSE.sat <- mean((y.predict - xy.splits.sat[['industry']][['y.test']])^2)
# 
# print(paste(i, ' Lasso MSE: ', MSE.lasso, ' Saturated MSE: ', MSE.sat))
# 
# summary(sat.model.bc)$coefficients
# as.data.frame(xy.splits.sat[['industry']][['X.test']]) %>% select(starts_with('`GroupOth'))

```


```{r}
# Compute R^2 from true and predicted values
eval_results <- function(true, predicted, df, p) {
  n = nrow(df)
  adj.RSS <- sum((predicted - true)^2)/(n-p-1)
  adj.TSS <- sum((true - mean(true))^2)/(n-1)
  adj.R_square <- 1 - adj.RSS / adj.TSS
  #RMSE = sqrt(RSS/n)
  
  return(c(Rsquare = adj.R_square))
}

#formula for adjusted R^2 found in following link.
#https://www.graphpad.com/guides/prism/latest/curve-fitting/reg_adjusted-r-squared.htm
```







```{r}
as.data.frame(lasso.best.lambda.train.pred) %>% mutate(Avg_in_dollars = (lasso.best.lambda.train.pred*lambda.bc+1)^(1/lambda.bc))
```

```{r}
income.sat.data.split <- test_train_split(income.dummy.bc, Avg.bc ~ .)
income.sat.data.split[['X.train']]

sat.model.bc <- lm(Avg.bc ~., data = as.data.frame(cbind(income.sat.data.split[['X.train']], income.sat.data.split[['y.train']])))
summary(sat.model.bc)

calc_MSE(sat.model.bc, as.data.frame(income.sat.data.split[['X.test']]), income.sat.data.split[['y.test']])


sat.y.predict <- predict(sat.model.bc, newdata = as.data.frame(income.sat.data.split[['X.test']]))
mean((sat.y.predict - income.sat.data.split[['y.test']])^2)
```

